math final Flashcards by Arielle Nemes

completing the square formula

(b/2) squared

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exponential formula

y= a(b) to the power of x

a represents y intercept, b represents growth/decay

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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

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remember to always first try and find the _____ when factoring

gcf

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what does open circle represent

less than or greater than/not included

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what kind of line is a less than greater than

dotted

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what does closed circle represent

less than or equal to, greater than or equal to/included

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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

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when 2 sides of an inequality equal each other, such as 10a -8 is greater than 10a -8, there are ______

infinite solutions

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when you multiply or divide a neg number in a inequality, you _____

flip the sign

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what is an empty set

a set that contains no elements- the empty set is a subset of every set

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what is the universal set

the largest set you are using

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what is the complement of a set

the set of all the elements in the universal set that are NOT in the set

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ex: what are the subsets of {3,4,5}

{3,4} {3}{4}{4,5}{3,5}….

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rate of change aka

slope

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function rules:

x values cannot repeat
one output per input
y values can repeat

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linear function equation

y=mx+b

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what is a nonlinear function

a function whose graph is not a line or part of a line

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what is a continuous graph

a graph that is unbroken

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what is a discrete graph

a graph composed of distinct, isolated points

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relation uses:

domain and range

relations may or may not be a function

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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

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h or v? y=5

horizontal

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h or v? x=6

vertical

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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

amount of increase or decrease -------------------------------------------- original amount

percent increase

new amount- original amount --------------------------------------- original amount

percent decrease

original amount- new amount ----------------------------------------- original amount