Unit 1

slope intercept form: y=mx+b

point-slope form: y-y1=m(x-x1)

slope formula: y2-y1/x2-x1

vertical translation: y=f(x)+K

horizontal translation: y=f(x-h)

reflection in x-axis: y=-f(x)

reflections in y-xis: y=f(-x)

vertical stretch/shrink: y= a*f(x) stretch: a>1 shrink: 1>a>0

horizontal stretch/shrink: y=f(ax) by a factor of 1/a stretch: 1>a>0 shrink: a>1

< dashed ≤ solid boundary

Unit 2

open circle: (

closed circle: [

vertex form: a(x - h)² + k

• aos: x=h

• vertex: (h,k)

standard form: y = ax² + bx + c

• aos: x= -b/2a

• vertext: f(-b/2a)

Intercept Form:f(x) = a(x - p)(x - q)

• aos: x= p+q/2

• vertex: p+q/2 , f(p+q/2)

Unit 3

If r is a positive real number, then √-r = i√r

a = real part,  bi = imaginary part
standard form of a complex number: a+bi

perfect square thing: c=(b/2)²

quadratic formula: x = − b ± b 2 − 4ac/2a

Unit 4

long division answer format: quotient + remainder/divisor

If a polynomial f(x) is divided by x - k, then the remainder is r = f(k)

p= factor of a constant term / q= factor of a leading coefficient

The Fundamental Theorem of Algebra:

If f(x) is a polynomial of degree n where n > 0, then the equation f(x) = 0 has at least one solution in the set of complex numbers.

Corollary:

If f(x) is a polynomial of degree n where n > 0, then the equation f(x)  = 0 has exactly n solutions provided each solution repeated twice is counted as two solutions, each solution repeated three times is counted as three solutions, etc. 

-An nth degree polynomial function f has exactly n zeros. 

Descartes rule of signs:

The number of positive real zeros of f is equal to the number of changes in sign of the coefficients of f(x) or is less than this by an even number.

The number of negative real zeros of f is equal to the number of changes in sign of the coefficients of f(-x) or is less than this by an even number.

zero: k is a zero of the polynomial function f

factor: x-k is a factor of the polynomial

solution: k is a solution (or root) of the polynomial equation f(x) = 0

x-intercept: if k is a real number, then k is an x-intercept of the graph of the polynomial function f. the graph of f passes through (k,0)

Location Principle:

If f is a polynomial function and a and b are two real numbers such that f(a) < 0 and f(b) > 0 then f has at least one real zero between a and b

the graph of every polynomial function has at most n-1 turning points

if a polynomial of degree n and n distinct real zeros then its graph has exactly n-1 turning points

a function is even when f(-x)=f(x)

a function is odd when f(-x)=f(-x)

if a polynomial function y=f(x) has degree n, then nth differences of function values for equally-spaced-x-values are nonzero and constant

conversely, if the nth differences of equally-spaced data are nonzero and constant, then the data can be represented by ba polynomial function of degree n