3 DECK SCRAMBLE Flashcards
1
Q
what is a coefficient?
A
the number in front of a variable or variables
2
Q
f(x) = ax^2 + bx + c What is the coefficient of the linear term?
A
b
3
Q
f(x)= 2(x+4)^2-3 What is vertex and which way does it open?
A
at (-4, -3) and it opens upwards (has min)
4
Q
why are roots called “zeros”
A
because it is where the height is zero; where the y value is zero; they are the x values that make the y=0
5
Q
What is the x intercept of a line? (what are the coordinates?)
A
Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )
6
Q
how do you find “probability”
A
experimental: (#successes)/(total # tries).
theoretical: (# successful outcomes) / (# total possible outcomes)
7
Q
When are there no solutions to simultaneous equations?
A
when the lines don’t cross, when they are parallel (no overlap)
8
Q
When completing the square and “a” is not equal to 1, what do you have to do?
A
divide both sides of equation (every term) by that “a” to turn “a” into “1”
9
Q
f(x)= -2(x-5)^2- 3What is vertex and is it a min or a max? What is the axis of symmetry?
A
at ( 5, -3) and it is a maximum, the AOS is x=5
10
Q
what is the constant term’s exponent on the x?
A
0
11
Q
How do you get the probability of taking a certain route on a tree diagram?
A
multiply the branches along the path till the end. write it at the end of the branch.
12
Q
How can you tell if the point (5, -3) is a solution to a linear equation?
A
If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.
13
Q
When is there and infinite number of solutions to simultaneous equations?
A
when they are the same line, then all points on the line satisfy both equations
14
Q
one out of four is _____ or ____%
A
0.25 or 25%
15
Q
three out of five is ____ or ____%
A
0.6 or 60%
16
Q
f(x)= 5 - 2x +3x^2 What is a, b and c ?
A
a = 3, b = -2, c = 5
17
Q
What are the fractional equivalents of these popular decimals:
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
A
1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
18
Q
change the probability of 3/5 to a decimal and a percent
A
0.6 or 60%
19
Q
What is the zero product property?
A
(this)(that)=0 is true when (this)=0 and when (that)=0. this is what we use when solving by factoring.
20
Q
change the probability 40% to a decimal
A
0.4
21
Q
Explain what a parabola with two real roots (real zeros) looks like.
A
crosses x axis at those roots, at those x values
22
Q
How do you solve by isolating the x^2 ? (when can you do it?)
A
When there is no linear term (no x term), simply act like you’re solving for x, but solve for x2 and in the last step, take square root of both sides ( + / - )
23
Q
change the probability 0.5 to a percent
A
50%
24
Q
What do we call b^2-4ac
A
the discriminant
25
can you have more than 100% of something?
YES.... if you have more than a whole. (but this can't be a probability)
26
what are the decimal equivalents of these popular fractions:
| 1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
27
change the decimal 0.0003 to a percent
0.03%
28
What are the roots of a function? (other names?)
the zeros, the x-intercepts, the solutions,where the parabola crosses
29
f(x) = ax^2 + bx + c What is the constant term?
c (it is the y intercept)
30
If an x intercept is 455, what point is on the line?
(455, 0)
31
what does a slope that is undefined look like?
vertical, straight up and down. The y axis has a slope of zero.
32
why is it called a constant term
alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height
33
What is the standard form of a quadratic?
ax2+bx+c = 0
34
How many diamonds in a deck of cards?
13
35
what is the quadratic term's exponent on the x ?
2
36
f(x)= 3x^2-6x+3 What is the constant term? what is the y intercept?
3, it is the also the y intercept
37
Why can't you divide by zero? (why can zero be in the top and not the bottom?)
10/2 asks "how many times do you add 2 to itself to get to 10?" the answer is 5.
10/0 asks "how many times do you add 0 to istelf to get to 10?" the answer is there is no answer. undefined
38
where is the vertex located?
on the axis of symmetry (highest or lowest point).
39
What are the three forms of a quadratic that we use?
standard: y = ax2-bx-c
factored: y = a (x-r) (x-r)
vertex: a (x-h)2 +k
40
How can you always get rid of fractions in any equation?
Multiply every term by the LCD (plop the LCD in the numerators, then simplify)
41
What is the gradient of a vertical line?
undefined
42
change the probability 0.04 to a percent
4%
43
one out of three is ____ or ____%
about .33 or 33%
44
how would you solve (3x-2)(x-5)=0 (what are solutions?)
set factors = 0 and solve: 3x-2=0 and solve x-5=0 zero product property. The solutions are x = { 5, 2/3}
45
what is tricky about the vertex form?
the -h part.. If its (x+9)2 +8 then h is -9.. remember that x=h is also the AOS !!!
46
What if you solve simultaneous equations all three ways, what will you notice?
they all give the same answer, the same POINT, (x,y)
47
If the discriminant is zero, what do you know about roots?
there is one double root, it is a perfect square, the parabola just touches down x axis without crossing, the vertex is on the x axis.
48
if there are 10 kids and you are choosing 3 to bring on a trip, how many ways can you do that? (perm or comb?)
Combination. nCr with n=10 and r=3
49
How do you show that a point lies on a line?
Show that, when you plug the point in, you get a true mathematical statement.
50
What are the solutions of a function? (other names)
the roots, the x intercepts, the zeros where the parabola crosses
51
How do you find the vertex of a parabola in standard form? y=ax^2+bx+c
the x value is always -b/2a . To get the y value for it, put that x value into the function and solve
52
what is the tough thing about quadratics?
the fact that they are squared.. We have to undo that x2. We want to get it linear!!
53
What does (A')' look like when shading?
double negative. (A')' = A, so the entire A circle should be shaded.
54
What is the x coordinate for all y-intercepts?
zero. all y intercepts are in the middle, not left or right, because they are on the y axis.
55
How do you solve by factoring?
get stuff all on one side, factor, set each factor = 0, solve each linear equation.
56
f(x) = a(x-h)^2 + k where it the vertex? what is the Axis of Symmetry?
vertex at the point (h, k), the AOS is the vertical line x= h
57
When you shade a VENN diagram, what does A U B look like?
Both circles and the overlap are all shaded (everything inside)
58
Perpendicular lines have _____ gradients, or slopes
OPPOSITE SIGN AND RECIPROCAL
59
How do you convert from vertex to standard form?
square the binomial and combine stuff
60
What does the discriminant tell us about?
about the roots, the zeros, how many x intercepts the parabola has, how many times it crosses the x axis, whether roots are real or imaginary
61
change the probability of 2/3 to a decimal and a percent
about .67 or 67% (.66666666666)
62
What is the "general" form of a line?
Ax + By = C no fractions.
63
what is the "most popular" form of a line?
gradient intercept (slope intercept)
64
What does the quadratic formula say about finding the x intercepts? (stand where and do what?)
stand at the AOS and reach up and down a bit to find the solutions
65
Geometrically, how is the shape of a parabola made?
A parabola is the set of all points equidistant from point, called the focus, and a line, called the directrix.
66
How many kings in a deck of cards?
4
67
Describe what an axis of symmetry is
it is where the parabola can fold onto itself. It is the equation of this vertical line, so you write "x = ___"(-b/2a)
68
f(x) = a(x-h)^2 + k How do we know if it opens up or down?
by the sign of a, if its positive, up, negative , down
69
what is the slope of a line that goes straight up and down?
undefined
70
when you are given a two way table, what should you always do?
PUT IN THE TOTALS ON SIDE and BOTTOM and the OVERALL TOTAL IN THE CORNER
71
what is the probability of getting 3 tails in a row flipping a coin?
1/2 x 1/2 x 1/2 = 1/8
72
one out of ten is _____ or ____%
0.1 or 10%
73
What are the zeros of y=5(x-3)(2x+1)
The zeros, or roots, or x intercepts are at(3, 0) and (-1/2, 0)
74
What is the discriminant?
b2-4ac (notice there is no sq root on it!!)
75
If the discriminant is zero, how many times does the parabola hit the x axis?
1. hits it and bounces off.
76
How is the axis of symmetry hidden in the quadratic formula?
it is the beginning.. (put both parts over 2a).. -b/2a
77
What is the quadratic formula?
x = -b +- sqroot b squared - 4ac all over 2a (but in formula)
78
f(x)= 3x^2-6x+3 What is the coefficient of the linear term?
-6 this is also known as "b"
79
What is the gradient-intercept form?
y = mx + c
80
f(x)= 3x^2-6x+3 What is the linear term?
-6x
81
what is the linear term's exponent on the x ?
1
82
change the probability of 1/4 to a decimal and a percent
0.25 or 25%
83
What is the gradient of a horizontal line?
ZERO
84
How do you solve simultaneous equations by substitution?
isolate a variable. SUBSTITUTE into the other equation, solve, then sub back in to find (x,y)
85
What is the symbol that joins two sets together into one set?
A big U , stands for UNION
86
how can you think of 150% of something?
150% of a pizza is one and a half pizzas!! (this can't be a probability)
87
What numbers can represent a probability?
Always between 0 and 1, examples: 0, .75, .05, 1, .35
88
change the decimal 0.03 to a fraction
3/100
89
f(x)= -4x^2 + 8 What is a, b and c ?
a = -4, b = 0, c = 8
90
What does A' mean?
The elements not in A
91
how would you solve 4x^2 - 9 = 13 ? (just say what you'd do)
no linear term, so just isolate the x2 and root sides
92
What is the probability of randomly taking one card and getting a diamond from a deck?
13/52 or 1/4
93
f(x) = ax^2 + bx + c What is the coefficient of the constant term?
c (it is the y intercept)
94
change the decimal 0.0003 to a fraction
3/10000
95
What is the y intercept of a line? (what are the coordinates?)
Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )
96
What is a midpoint?
the point halfway along a segment. right in the MIDDLE
97
f(x)= -4x^2 + 8 What is the axis of symmetry?
x= -b/2a = -0/2(-4) = 0/8 = 0. AOS is x=0, which is the y axis!!
98
change the probability of 1/3 to a decimal and a percent
about .33 or 33% (.33333333333)
99
If the discriminant is negative, what do you know about roots?
there are no real roots, 2 imaginary roots, the parabola doesn't touch x axis
100
change the probability of 1/2 to a decimal and a percent
0.5 or 50%
101
How do you find the midpoint between two given points?
the midpoint has an x and y value, (x,y). the X value is the average of the two x values, and the Y value is the average of the two y values.
102
change the probability of 2/5 to a decimal and a percent
0.4 or 40%
103
How would you solve 9x^2 - 3x = 0 ? (just say what you'd do)
factor out x and set factors=0.. (one solution will be 0)
104
What is a perpendicular bisector?
the line that goes through the midpoint of a segment, and it is also perpendicular to it.
105
Explain what the graph of a parabola with no real roots (real zeros) looks like.
doesn't touch x axis
106
If a line as a slope of -5, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___
-5 and perp 1/5
107
why is it called a discriminant?
because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)
108
What are the zeros of a function? (other names?)
the roots, the x intercepts, the solutions, where the parabola crosses
109
When is there just one solution to simultaneous equations?
when they cross (at one point)
110
How can you think of %
PER 100 (or, divided by 100)
111
What are the five ways to solve a quadratic?
set to zero and factor, complete square, quadratic formula, graph and look for x-intercepts, or when there is no linear term, isolate the x2 and root both sides.
112
What is the graph of a line showing us? (or a graph of a parabola or any function)
It is showing us all of the points, (x,y), that make the equation true. Every dot on the graphed line will make the equation true, they all work.
113
What is the slope of a line in standard (general) form?
-A/B
114
Are all quadratics similar?
YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..
115
thinking of the quadratic formula, why are there no real roots when you have a negative discriminant?
because you have to take the square root of a negative, which is an imaginary number. You end with an imaginary number.. .hence.. Imaginary roots (not real)
116
How do you find the average of two numbers?
add them up and divide by 2
117
change the decimal 0.03 to a percent
3%
118
If A = { 1, 2 }, how many elements does A have?
two
119
When you graph a line or a parabola, what are you actually graphing?
THE SOLUTION! Those are all of the points that make the equation true. All of the points that "work". If you put any other pionts, (x,y) into the equation, they wont work, You will get a false statement.
120
What do students forget about OR ?
The OR BOTH part. The union of A and B are all of the elements in A, in B and also the ones that are in BOTH.
121
If we are given an x, like x=5, and need to fine a y that goes with it, how do we find it?
substitute the 5 in for the x in the eqution and solve for y, That y value goes with the 5. The point (5, y) will be on the line.
122
How can you tell if the point (5, -3) is on a line or a parabola if you are given the equation?
If it "works." Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.
123
Why do parabolas look different if they are all similar?
Well.... Simply either imagine zooming way in or zooming way out... this method can always get any 2 parabolas to look the same.
124
If A = { 1, 2, 6} , what is n(A) ?
n(A) is the number of elements in A. In this case, n(A)= 3
125
where is the combination button on the calculator?
Math > PRB then down to nCr
126
What is the gradient formula? (the slope formula?)
m = ( y - y ) / ( x - x )
127
AND goes with ______ [union or intersection]
intersection
128
change the probability of 1/5 to a decimal and a percent
0.2 or 20%
129
What is solution to:5(x-8)(x+3)=0
8 and -3.
(this)(that)=0 situation
this=0 and that=0
we are looking for the x values that make the equation true.. so we want to make x-8=0 and x+3=0
130
Why is it called "gradient-intercept" form? (slope-intercept)
There is a gradient and a slope explicitly shown in the formula
131
three out of ten is ____ or ____%
0.3 or 30%
132
If the discriminant is positive, how many times does the parabola hit the x axis?
2
133
How do you graph a quadratic in standard form?
| f(x)=ax^2+bx+c
first graph the Axis of symmetry with dotted line, (x= -b/2a) then make a T table and use that x value to find the vertex and use a couple integers near it to find other points. LEAVE SPACE FOR ARITHMETIC. Reflect over the AOS and connect the dots
134
what are the coordinates of a point?
(x,y), the x and y value.
135
What is a slightly different form of the general form you may be asked to write an equation in?
Ax + By + D = 0 in stead of Ax + By = C
136
What are the fractional equivalents of these popular percents:
50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%
1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000
137
If you have 3 pairs of shoes, two pairs of pants and 4 shirts.. how many outfits?
3*2*4= 24 outfits
138
INTERSECTION goes with _____ [OR or AND]
AND
139
If you are given two points and need to find the equation of a line, how do you do it?
First, fine the gradient using m=(y-y)/(x-x), then use that gradient and EITHER OF THE POINTS. Put it in point gradient form. (point slope form)
140
How do you know when a parabola is smiling?
when a is positive
141
What are the x intercepts of: y=5(x+6)(x-3)
at -6 and at 3(they are also called solutions or zeros)
142
If a y intercept is 990, what point is on the line?
(0, 990)
143
If the discriminant is positive, what do you know about roots?
there are 2 real roots, and the parabola crosses x axis twice..at these roots
144
change the decimal 0.3 to a percent
30%
145
f(x)= -4(x-8)^2+6What is vertex and which way does it open?
| what is AOS?
at (8, 6) and opens downward (has max). The AOS is x=8
146
the number 5/0 is equal to :
undefined
147
How many cards in a deck of cards?
52
148
What is solution to:g (x+f)(x-w) = 0
-f and w(this)(that)=0 situationthis=0 and that=0we want to make equation trueso we solve x+f=0 and x-w=0
149
With two simultaneous linear equations, what are the three options for a solution?
No solution, one solution, or an infinite number of solutions.
150
What does (A U B)' look like when shading?
shade just the area outside of the circles.
151
How do you find the max or min value of a quadratic in either form?
it is the y value at the vertex. In vertex form, it's simply k. In standard form, Plug -b/2a into the function to get y.remember to look at "a" + smiles have min.. - frowns have max. OR PUT IN YOUR CALCULATOR AND USE MAX MIN FINDER.
152
If you know that a quadratic has x intercepts at 5 and 3, , what is the factored form?
What is the equation of AOS?
factored form: y = a (x-3)(x-5)
aos: x=4
notice aos is average of 3 and 5
(3+5)/2 = 4
153
two out of five is ____ or ____ %
0.4 or 40%
154
How do you know when it is a quadratic?
when the highest degreed term is the x^2 term (quadrus:square)
155
what completes the square and what is the factored form? x2 + 6x + ____
9 completes it and the factored form is (x+3)^2
156
What is the probability of randomly picking one card a red card from a deck?
26/52 or 1/2
157
What is the gradient of a flat (horizontal) surface?
ZERO
158
How do you solve simultaneous equations by elimination?
organize equations so they line up nice. Get coefficients to be opposites. Add equations and solve. Then sub back in to find (x,y)
159
On a number line, what is the midpoint between 8 and 12?
at the average: 10. 10 is halfway between 8 and 12. add and divide by 2. 8+12=20. 20/2= 10
160
change the probability 0.8 to a percent and a fraction
80% and 4/5
161
What are the decimal equivalences of these popular percents?
| 50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001
162
Parallel lines have ______ gradients, or slopes
the same
163
change the decimal 0.003 to a fraction
3/1000
164
two out of three is ____ or ____%
about .667 or 66.7%
165
If the discriminant is negative, how many times does the parabola hit the x axis?
0
166
If there are 10 kids and you are choosing a president, vp and treasurer, how many ways can you do that? (perm or comb)
Permutation. nPr with n=10 and r=3
167
How do you solve simultaneous equations by graphing?
| what if they are quadratics?
graph both lines and look for the intersection, the solution is the coordinates (x,y) If they are quadratics they could have 2 intersections.
168
Why does AND go with INTERSECTION? A ∩ B = A and B
Because you have to be a member of both A and a member of B to be a part of A ∩ B
169
f(x)= 3x - 9 What is a, b and c?
a = 0 , b = 3, c = -9..There is no quadratic term..
THIS IS LINEAR!!!
IT'S A LINE!
slope of 3
170
What is the solution to simultaneous equations? (system of equations?)
The set of points that satisfies (makes true) all of the equations in the system. In algebra 1, this is just ONE POINT, (x,y), But we will solve quadratic-linear systems that will have 2 solutions.
171
change the probability of 1/10 to a decimal and a percent
0.1 or 10%
172
What are the x intercepts of a function? (other names?)
the roots, the zeros, the solutions
173
What fractions can represent a probability?
Any fraction as long as the top is smaller than the bottom (or equal). IT CAN'T BE TOP HEAVY!
174
When can you just isolate the x^2 and root both sides?
when there are no linear terms (only quad and const)
175
What is the symbol that just takes the overlap of two sets?
An upside down U, look like this: ∩, INTERSECTION
176
f(x) = ax^2 + bx + c What is the linear term?
bx (the term is the whole thing)
177
thinking of the quadratic formula, why are there 2 real roots when the discriminant is positive?
because there is a square root of a positive, you will have to + and - that in the top, giving 2 different real solutions.
178
What are the gradients (slopes) of the diagonals of a square?
+1 going up L to R, and -1 going down from L to ROW
179
f(x)= 6x^2- 7x What is a, b and c ?
a = 6, b=-7, c = 0
180
What is a way to help shading in VENN diagrams?
Label the areas 1, 2, 3 and 4. Let A= {1,2} B= {2,3} , intersection is {2} and outside of the circles {4).
181
f(x)= (x+9)^2-8 What is vertex and is it a min or a max?
at (-9, -8) and it is a minimum
182
How could simultaneous quadratic equations have no solutions?
two parabolas curving away from eachother and never crossing is one possibility.
183
Does "a" have to be equal to 1 when completing a square?
YES
184
if you know that the x intercepts of a parabola are at (-3, 0) and (9,0), what is the factored form and what is AOS?
factored form: y= a (x+3) (x-9)
aos at x = (-3+9) / 2 = 6/2
aos at x=3
185
What are simultaneous equations? (system of equations)
a group of equations
186
f(x)= 3x^2-6x+3 What is the coefficient of the constant term?
3 this is also known as "c"
187
What is the probability of randomly taking one card and getting a king from a deck?
4/52 or 1/13
188
f(x)= 3x^2-6x+3 What is the quadratic term?
3x^2
189
what is point-gradient form? (point slope)
A rearrangement of the gradient formula: y-y =m (x-x)
190
How can centimeters and a meter stick help you think of percent?
Think of centimeters as "PERCENTIMETERS".. each one is one percent of a meter. 35cm is 35% of a meter.
191
What are the three ways we solve simultaneous equations?
Graphing (and looking for intersection), substitution and elimination
192
How do you know when a parabola is frowning?
when a is negative
193
change the probability 0.5% to a decimal
0.005
194
How could simultaneous equations have exactly two solutions?
Imagine a line and a parabola. the line could cross the parabola twice.
195
What is an interesting fact about slopes between -1 and +1?
HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1 (and they are perpendicular)
196
When we graph a parabola to solve a quadratic, what do we look for?
look for the x intercepts, these are the roots. The zeros, the solutions
197
If a line as a slope of 2/3, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___
2/3 and perp -3/2
198
If there is no constant term, what is an easy way to factor?
just factor out the x and set the factors to zero (one solution is zero)
199
four out of five is ____ or ____%
0.8 or 80%
200
why are they called "quadratics?"
from latin "quadrus" which means SQUARE
201
What do the probabilities on the branches leaving a single node in a tree diagram have to add to?
1. If you have two branches, then they should add to 1, if you have five branches from same node, all five added together should equal 1.
202
When you shade a VENN diagram, what does A ∩ B look like?
Just the overlap sliver in the middle is shaded.
203
With tree diagrams, what does MA.AD stand for?
Multiply across, Add down
204
What is the equation of the y axis?
x=0
205
If we are given a Y value, like y-8, and need to find the x that goes with it, how do you do it?
substitute the 8 in for the y in the equation and solve for x. That x goes with the 8. the point (x, 8) will be on the line.
206
What are solutions to (x+8)(x-3) = 0
x = { -8, 3} this is not a point on the graph, it is a set of two numbers that make the equation true. They are also the x intercepts of the parabola
207
can you have a probability of 5/3?
NO... that is more than 1
208
What does it mean to "satisfy" an equation?
Make the equation true.
209
What are the three forms of a quadratic function?
Standard y=ax^2+bx+c
Vertex y=a(x-h)^2+k
Factored y= a(x-r)(x-r)
210
What is the eqution of a horizontal line that goes through the y axis at 8?
How can you think about it to help you?
y = 8. Since y is the height, you can think of it as all of the points that have a height of 8. Also, you can think of it as all of the points that have a y value of 8, so you are a solution if your y value is 8.
211
Why is it called "point-gradient" form?
There is a point and a gradient explicitly shown in the form
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f(x)= 6x^2- 5x What is the axis of symmetry?
x= -b/2a = -(-5)/2(6) = 5/12, AOS x= 5/12
213
How do you find the equation of a perpendicular bisector?
Find the point and the gradient (slope) and put it in point-gradient form. The point is the midpoint (use averages) and the slope is the RECIPROCAL and OPPOSITE of the slope between the two given points.
214
can you have a probability of 3/5?
Yes, that's 60%
215
thinking of the quadratic formula, why is there only one real root when the discriminant is zero?
because the square root of zero is zero, so you are going to + and - zero... the quad formula reduces to -b/2a .. The only root is the axis of symmetry (the vertex is on the x axis)
216
change the probability of 0.45 to a percent
45%
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change the probability 0.04% to a decimal
0.0004
218
How do we handle that squared term? how can we undo it?
by either splitting the x's apart by factoring, or by taking a square root somewhere..
219
What is the equation of the axis of symmetry?
x = -b / 2a
x= opposite b / twice a
(notice it is the equation of a vertical line)
220
Does "a" have to be equal to 1 when doing quadratic formula?
NO
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How do you know if a parabola in standard form opens upward (smile) or down (frown)?
if "a" is pos it opens up. if a is negative, it opens down. Positive people smile, negative people frown.
222
change the probability 0.0003 to a percent
0.03%
223
can you have a probability of 0.5?
Yes, that's 50%
224
How do a lot of people think about the gradient
| (the slope)?
rise/run... or change in y / change in x
225
Can you have a probability of 3.5?
NO. probabilities are between 0 and 1
226
change the probability of 3/4 to a decimal and a percent
0.75 or 75%
227
What is probability?
The likelihood of an event happening.
228
can you have a percent of 5/4 ?
YES! that would be 125%..... (this can't be a probability)
229
one out of five is ____ or ____%
0.20 or 20%
230
change the decimal 0.003 to a percent
0.30%
231
Explain what a parabola with one real root (real zero) looks like.
just touches x axis at one spot, the root (the zero), it doesn't cross it, it bounces off it, called a "double root", the vertex is on the x axis
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How do you know if a parabola has a max or minimum by looking at the function in standard form?
if " a" is pos, it has a min. if 'a' is negative, it has a max
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what completes the square and what is the factored form? x^2 - 8x + ____
16 completes it and the factored form is (x-4)^2
234
f(x) = a(x-h)^2 + k
How do we know if it has max or min?
what is the AOS?
by the sign of a, if its positive it opens up so it has a MIN, negative it opens down so it has a MAX.
aos at x=h
235
change the probability of 4/5 to a decimal and a percent
0.8 or 80%
236
How do you solve by completing the square?
get all quadratic and linear term on one side and bring constant term over to other.... Make sure a=1, take half of b and square it, add it to both sides. Factor, root, solve
237
what does a slope of zero look like?
horizontal, flat from left to right. The x axis has a slope of zero.
238
What is the gradient of a line?
the slope, the steepness
239
UNION goes with ______ [OR or AND]
OR
240
What is the the difference between theoretical and experimental probability?
theoretical is from thinking of all of the possibilities and doing it with math, experimental is the #successes/total attempts you observe.
241
Why is it called a "linear" term
alone its graph would be a straight line
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What is the y coordinate for all x-intercepts?
zero. all x intercepts have a height of zero because they are on the x axis.
243
the number 0/5 is equal to :
zero. 0
244
Do all quadratic functions have x intercepts?
No, some don't touch the x axis.. These have imaginary roots and a negative discriminant
245
Difference between a Permutation and a Combination?
Permutation is choosing and Placing in a Particular Place, Combinations are just choosing
246
what is difference between (3, -2) and {3, -2}
the first is a point on a plane (over 3, down 2) and is in parentheses... The second set are numbers in braces, so it is simply a set containing two values, 3 and -2. It is not a point on a plane, the order does non matter in braces.
247
What is the midpoint of (4, 5) and (6, 15). (think, the average of 4 and 6, and the average of 5 and 15
average of 4 and 6 is 5. the average of 5 and 15 is 10. so at (5, 10)
248
f(x) = ax^2 + bx + c What is the coefficient of the quadratic term?
a
249
What is the equation of the x axis?
y = 0
| all horizontal lines are in the form y=something
250
What is a solution to an equation?
A solution is the set of values that makes an equation TRUE.
251
How can you find the x intercepts from an equation of a line?
Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)
252
How can you find the y intercepts from an equation of a line?
Plug zero in for X and solve for Y. The coordinates wll be (0, Y)
253
Why does OR go with UNION, ex. A U B = A or B
Because you are part of the union as long as you are a part of A or B or BOTH
254
f(x)= 3x^2-4x+5 What is a, b and c ?
a = 3, b = -4, c = 5
255
change the probability 5% to a fraction
1/20 (one out of 20)
256
change the decimal 0.3 to a fraction
3/10
257
The three forms of equations of a line we use are :
point-gradient form, gradient-intercept form, general form
258
f(x) = ax^2 + bx + c What is the quadratic term?
ax2
259
f(x)= 3x2-6x+3 What is the axis of symmetry?
-b/2a = -(-6)/2(3) = 6/6 = 1
260
What is the vertex form of a quadratic?
f(x) = a(x-h)^2 + k
261
If there is no linear term, what is an easy way to solve?
simply isolate the x^2 and root both sides.
262
OR goes with______ [union or intersection]
union
263
one out of twenty is ____ or _____%
0.05 or 5%
264
How can you think of a slope of 1 or -1?
A perfect diagonal of a square, 45 degrees!
265
change the probability of 1/8 to a decimal and a percent
0.125 or 12.5%
266
In general, what are we looking for with two simultaneous linear equations?
THE INTERSECTION! (X, Y) ! the intersection is the solution, it is the point that makes both equations true, it satisfies both equations.
267
What is the equation of a vertical line that goes through the x axis at 7?
How can you think of that line to help make sense of it?
x = 7. You can think all of the points that are over 7 to the right.. or "all of the points on this line have an x value of 7, so you are a solution as long as your x=7.
268
where is the permutation button on the calculator?
Math > PRB then down to nPr
269
Do all quadratics have a y intercept
YES... All quadratics have exactly 1 y-intercept.. (c).. if there is no constant term, the y intercept is 0, so the parabola passes through the origin!!!!
270
f(x)= 3x^2-6x+3 What is the coefficient of the quadratic term?
3 this is also known as "a"
| notice that 3x^2 is the entire quadratic term, 3 is just he coefficient.
271
change the probability of 6% to a decimal
0.06
272
How can you always find the y intercept of a line?
plug zero in for x and find the y. y intercept at (0, y)
273
how can you always find the x intercept of a funciton
plug zero in for y and find the x or x's. x intercept at (x,0)
274
what are the three forms of a linear equation?`
standard (general): Ax + By + C = 0
slope (gradient) intercept: y = mx + b
point - slope (gradient): y-y = m (x-x)
275
How can you use calculator to find aos?
Graph the parabola, then use MAX or MIN. the x value is the AOS.
276
What is a cool feature you can use when tracing along a graph on your calculator?
While tracing, you can type any x value and it will give you the y value for that x , and hence, the coordinates (x,y)
277
what does the line y=x look like?
an uphill diagonal of a square. It goes from bottom right to top left.
278
what does the line y= - x look like?
A downhill diagonal of a square. It goes from top left to bottom right.
279
What does line y= -4 look like?
a HORIZONTAL (left to right) line through y=-4. It is below the x axis. All of the points on the line have a y value of -4.
280
What does the line x = 8 look like?
a VERTICAL line (up and down) through x = 8. it is to the right of the y axis. All of the points on the line have an x value of 8.
281
what is the equation of the x axis?
y = 0 (all of the points on x axis have a y value of zero)
282
what is the equation of the y axis?
x = 0 (all of the points on the y axis have an x value of zero)
283
what does y=0 look like?
It is the x axis. all of the points on x axis have a y value of zero.
284
what does x=0 look like?
It is the y axis. All of the points on the y axis have an x value of zero.
