math final Flashcards
completing the square formula
(b/2) squared
exponential formula
y= a(b) to the power of x
a represents y intercept, b represents growth/decay
how to find zeros of function on calc
called the zero product property
plug function into calc, go to split screen table, and find x’s that have y as zero. Ex: (9,0) (4,0). 9 and 4 would be the zeros
remember to always first try and find the _____ when factoring
gcf
what does open circle represent
less than or greater than/not included
what kind of line is a less than greater than
dotted
what does closed circle represent
less than or equal to, greater than or equal to/included
when putting inequalities on a number line such as x is greater than 7, or 15 is less than 7, the number line’s line will point in the ______ direction of the less than/greater than symbol. If its less than/greater than, the circle is _____
opposite
open
when 2 sides of an inequality equal each other, such as 10a -8 is greater than 10a -8, there are ______
infinite solutions
when you multiply or divide a neg number in a inequality, you _____
flip the sign
what is an empty set
a set that contains no elements- the empty set is a subset of every set
what is the universal set
the largest set you are using
what is the complement of a set
the set of all the elements in the universal set that are NOT in the set
ex: what are the subsets of {3,4,5}
{3,4} {3}{4}{4,5}{3,5}….
rate of change aka
slope
function rules:
x values cannot repeat
one output per input
y values can repeat
linear function equation
y=mx+b
what is a nonlinear function
a function whose graph is not a line or part of a line
what is a continuous graph
a graph that is unbroken
what is a discrete graph
a graph composed of distinct, isolated points
relation uses:
domain and range
relations may or may not be a function
point slope form equation
y-y =m(x-x )
1 1
y sub 1 is y coordinate, m is slope, x sub 1 is x coordinate
h or v? y=5
horizontal
h or v? x=6
vertical
standard form equation
ax + by =c
the x intercept is
where the line crosses the x axis
the y intercept is
where the line crosses the y axis
to find x intercept
plug in zero for y and solve
to find y intercept
plug in zero for x and solve
positive line is
low to high
negative line is
high to low
y = IxI + 2 means
up 2
y = IxI -2 means
down 2
y = Ix+2I means
left 2
y = Ix-2I means
down 2
perpendicular line means
negative reciprocal of other line’s slope
parallel line means
same slope different y intercept
domain
x values,
range
y values
horizontal line is
zero
vertical line is
undefined
how to solve line of best fit
write for the equation, by finding slope using point slope form, then converting that into slope intercept form
linear equations: one solution
two lines that intersect at one point
linear equations: infinitely many solutions
two equations have same line
linear equations: no solution
parallel lines
exponential growth
b is GREATER THAN 1 (1 + %)
exponential decay
b is LESS THAN 1 (1 - %)
compound interest formula
A = P(1+ r/n) to the nt power a= balance/what we are looking for p=inital amount r= annual rate (expressed as decimal) n= number of times interest is compounded per year t= time in years
monomial
1 term
binomial
2 terms
trinomial
3 terms
polynomial
4 and up terms
constant
degree of zero
linear
degree of one. ex: 4x + 2. number of highest exponent)
quadratic
2
degree of 2. ex: 4x. +2 (number of highest exponent)
cubic
3
degree of 3. ex: 4x. +2 (number of highest exponent)
fourth degree
4
degree of 4. ex: 4x. +2. (number of highest exponent)
roots mean
zeros
linear functions
common difference between y values
ex: 2, 5, 8
+3 +3
straight line
exponential functions
common ratio: multiplying by the same value overtime for each y value
ex: 0.25, 0.5, 1,
x2 x2
slight curve
quadratic functions
second set has common difference
ex: 1, -1, 1, 7, 17
-2 +2 +6 +10 first differences
+4 +4 +4
parabola
axis of symmetry
-b/2a
minmum
a is less than zero. shaped like upside down u
maximum
a is greater than zero. shaped like: U
If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point ______
(h,k)
the closer a is to zero, ______
the wider the graph
mode
value that appears the most
mean
average
uniform
all the bars on histogram are about the same height
symmetric
peak is at center of histogram
skewed
peak is to the side of histogram
communative property
changing the order doesn’t change the sum. ex: a + b = b + a
associative property
part of a group, order doesn’t matter ex: (a + b) + c = a + (b + c)
identity property
the sum of any real number 0 is original number.
the product of any real number and 1 is the original number
percent change
original amount
percent increase
new amount- original amount
—————————————
original amount
percent decrease
original amount
