scramble test questions Flashcards
What are the three forms of a quadratic function? GIVE NAMES AND EXAMPLES
standard y=ax2+bx+c
vertex y=a(x-h)2+k
factored y=a(x-r)(x-r)
What are the three forms of a linear function? GIVE NAMES AND EXAMPLES
standard: Ax+By=C
point slope: y-y=m(x-x)
slope intercept: y=mx+b
what does y=-x look like
a diagonal going from upper right down to lower left, through origin
When you graph a line, 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.
what is the slope of a line that goes straight up and down?
undefined
f(x) = ax2 + bx + c What is the quadratic term?
ax2
What is the gradient of a line?
the slope, the steepness
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.
Explain what a parabola with two real roots (real zeros) looks like.
crosses x axis at those roots, at those x values
When is there just one solution to simultaneous equations?
when they cross (at one point)
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
When is there and infinite number of solutions to simultaneous equations?
when they are the same line, then all points on the line satisfy both equations
How can you tell if the point (5, -3) is a solution to a linear 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.
what is the quadratic term’s exponent on the x ?
2
one out of twenty is ____ or _____%
0.05 or 5%
f(x)= 2(x+4)2-3 What is vertex and which way does it open?
at (-4, -3) and it opens upwards (has min)
What is the symbol that joins two sets together into one set?
A big U , stands for UNION
What are the x intercepts of a function? (other names?)
the roots, the zeros, the solutions
change the probability of 1/8 to a decimal and a percent
0.125 or 12.5%
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)
What is the zero product property?
(this)(that)=0 is true when (this)=0 and when (that)=0. this is what we use when solving by factoring.
where is the vertex located?
on the axis of symmetry (highest or lowest point).
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)
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}
What is the eqution of a horizontal line that goes througyh 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.
Perpendicular lines have _____ gradients, or slopes
OPPOSITE SIGN AND RECIPROCAL
How could simultaneous equations have exactly two solutions?
Imagine a line and a parabola. the line could cross the parabola twice.
What is the gradient of a vertical line?
undefined
How do you find the midpoint between two given points?
the X value is the average of the two x values, and the Y value is the average of the two y values.
the number 5/0 is equal to :
undefined
what is the constant term’s exponent on the x?
0
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
What are the three ways we solve simultaneous equations?
Graphing (and looking for intersection), substitution and elimination
change the probability 0.5% to a decimal
0.005
What do we call b2-4ac
the discriminant
What is the quadratic formula?
x = -b +- sqroot b squared - 4ac all over 2a (but in formula)
What is a solution to an equation?
A solution is the set of values that makes an equation TRUE.
why are roots called “zeros”
because it is where the height is zero; where the y value is zero; they are the x values that make the y=0
can you have a probability of 5/3?
NO… that is more than 1
What is the discriminant?
b2-4ac (notice there is no sq root on it!!)
What are the gradients of the diagonals of a square?
+1 going up L to R, and -1 going down from L to ROW
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)
What is solution to:5(x-8)(x+3)=0
8 and -3(this)(that)=0 situationthis=0 and that=0we are looking for the x values that make the equation true.. so we want to make x-8=0 and x+3=0
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!!!!
why are they called “quadratics?”
from latin “quadrus” which means SQUARE
When are there no solutions to simultaneous equations?
when the lines are parallel (no overlap)
What is the graph of a line showing us?
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.
With two simultaneous linear equations, what are the three options for a solution?
No solution, one solution, or an infinite number of solutions.
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)
Do all quadratic functions have x intercepts?
No, some don’t touch the x axis.. These have imaginary roots and a negative discriminant
what does a slope that is undefined look like?
vertical, straight up and down. The y axis has a slope of zero.
If the discriminant is zero, how many times does the parabola hit the x axis?
1
If the discriminant is negative, how many times does the parabola hit the x axis?
0
change the probability of 4/5 to a decimal and a percent
0.8 or 80%
How do you solve by factoring?
get stuff all on one side, factor, set each factor = 0, solve each linear equation.
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
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.
What does it mean to “satisfy” an equation?
Make the equation true.
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)
What is the equation of the y axis?
x=0
Parallel lines have ______ gradients, or slopes
the same
what is the equation of the x axis?
y=0
What is a perpendicular bisector?
the line that goes through the midpoint of a segment, and it is also perpendicular to it.
INTERSECTION goes with _____ [OR or AND]
AND
