math ch2 (2.10-2.20)

how to solve quadratic equations

how to determine the number of real roots (solutions) of a quadratic equations

the discriminant

if the discriminant is less than 0

if the discriminant is equal to 0

if the discriminant is greater than 0

vertex

what is the general form of the quadratic equation

if a is positive

if a is negative

what is the coordinate of the vertex

how to find the x coordinate of the vertex (formuila)

rational expression

rule of denominator in a rational expression

points of discontinuity

formula of domain of the rational expression:

rule for multiplying rational expressions

rule for dividing rational expressions

simplifying rational expressions

synthetic division

prime polynomial

adding or subtracting rational expressions (like denominators)

adding or subtracting rational expressions (unlike denominators)

complex rational expressions

remainder theorem

if f( r ) = 0, this means what for the remainder and factor

roots of a polynomial

number of roots are the number of

if a polynomial has a real root, the function on either side of the root with have

if the polynomial value is positive just before the root, it will be —— after the root

if the polynomial value is negative just before the root, it will be ——- after the root

if a complex number a + bi where b is not 0, is a root of the polynomial, the conjugate will be (form and answer)

sum of roots formula in a quadratic equation

product of roots in a quadratic equation

composite function form

what comes first in the composite function (f o g)

inverse functions

how to solve for inverse functions

whats the rule for domain and range in inverse functions

radical equations

radical equation formulae

whats true about the domain and range of radical equations

how to rationalize a denominator

multiply by its conjugate

if the index of the radical expression and the exponent of the radicand is evenbut the output is odd, we must use :

steps to solving the radical equation and inequalities

for any f(X)= a(X)/b(X), b(x)=/0, then a(x) and b(x) have no—— and could have

vertical asymptote if

horizontal asymptote if (two conditions)

there is no horizontal asymptote if:

f(X)= a(x) / b(x) if a (x)=1 and b(x)=x, then it is called the

talk abt the definition, vertical, and horizontal asymptote in f(x)= 1/x-h +k

direct variation

inverse variation

joint variation

combined variation