#### College Algebra

quadratic formula

compound interest formula

simple interest formula

distance formula

D=R X T

complex numbers

discriminant formula

if D> 0: 2 real solutions
if D<0: 2 non-real solutions
if D=0 : exactly 1 solution

factor by grouping

inequality signs

when the inequality sign changes

if you multiply or dividing both sides of the inequality by a negative number it changes the direction of the sign

when the inequality sign does not change

if you add or subtract both sides of the inequality

solving a compound inequality with and

it will involve the word and- first solve each inequality separately- then find the intersection of the two solution sets

interval notation of compound inequalities with the word or

will have the union sign U

greater/ less than or equal to

filled in circle

greater than/ less than

open circle

quadrants

midpoint formula

distance formula

standard form of a circle

center of the circle: (h,k)
radius: r

general form of a circle

converting general form to standard form

find the center, radius, and intercepts, rearrange the terms then complete the square then factor

positive slope

negative slope

zero slope

slope

m= rise/ run

point slope form

m: slope of the line

slope intercept form

m: slope
b: y intercept

standard form slope and y intercept

Ax + By = C slope: m= -A/B
y intercept: C/B

horizontal line equation

y = b b: the y coordinate of any point on the line

two non-vertical lines are parallel if

they have the same slopes

two non-vertical lines are perpendicular if

the product of their slopes is -1

vertical line test

when saying if a function is increasing, decreasing, or constant in interval notation use

parentheses and not brackets

even function

symmetric across the y axis

odd function

symmetric across the origin

constant function

identity function

square function: f(x)= x^2

cube function: f(x)= x^3

absolute value function: f(x)= lxl

square root function: f(x)= sqrtx

cube root function: f(x)= 3sqrtx

reciprocal function: f(x)= 1/x

greatest integer function

y= -f(x)

reflection about the x-axis

y= f(-x)

reflection about the y-axis

vertical stretch y= af(x)

multiply each y coordinate by a

horizontal compression

a>1: divide each x coordinate of y= f(x) by a

horizontal stretch

0<a<1: divide each x coordinate of y= f(x) by a

one-to-one function

a function is one-to-one if for any values a cant = b in the domain- can determine this using the horizontal line test

finding the inverse of a function

quadratic function

the porabola opens up if

the leading coefficient a>0

the porabola opens down if

the leading coefficient a<0

the standard form of a quadratic function

the vertex of a porabola: (h,k)

e

natural base

vertex formula

revenue equation

Revenue= Price x Quantity
R=PXQ

the right hand end behavior finishes up if

a>0

the right hand end behavior finishes down if

a<0

even degree end behavior

if the degree n is even the graph has the same left and right hand end behavior- it starts and finishes in the same direction

long division

synthetic division

can only be used if divided by form (x-c)

complex conjugate pairs theorem

when do vertical asymptotes occur

when the graph of a function approaches positive or negative infinity as x approaches some finite number a- cancel any common factors before locating the vertical asymptotes

if the degree of the denominator is greater than the degree of the numerator:
m>n

then y=0 is the horizontal asymptote

if m<n

then there are no horizontal asymptotes

if the degree of the denominator is equal to the degree of the numerator:
m=n

then the horizontal asymptote is y= an/bm

direct variation formula

y=kx
k: the constant of variation

inverse variation

joint variation formula

y=kxz

continuous compound interest formula

A: total amount after t years
P: original investment
r: interest rate per year
n: number of times interest is compounded per a year
t: number of years

method of relating the bases

if b^u= b^v then u=v