Precalculus: Algebra Lessons 2.1-2.3

standard form equation

f(x)=ax²+bx²+c

Vertex form?

f(x)=a(x-h)²+K

instantaneous rate of change?

S(t)=-1/2 gt²+V₀t+S₀

In the instantaneous rate of change equation what variable is height?

S(t)

In the instantaneous rate of change equation what variable is initial vertical velocity?

V₀

In the instantaneous rate of change equation what variable is the initial height?

S₀

What type of variation is a positive power?

direct variation

What type of variation is a negative power?

inverse variation

constant of variation equation?

f(x)=K ⊗ Xⁿ

What are even functions symmetrical to?

y-axis

What are odd functions symmetrical to?

origin

what quadrant is the graph in if K>0?

Q1

What quadrant is the graph in if K<0?

Q4

Odd function and positive LC?

↓↑

Odd function negative LC?

↑↓

Even function positive LC?

↑↑

Even function negative LC?

↓↓

odd multiplicity?

crosses x-axis

even multiplicity?

touches x'-axis

polynomial form

Quotient(divisor)+remainder

fraction form

Q+R/D

remainder theorem

if a polynomial f(x) is divided by f-k then the remainder r=f(k) (plug k into f(x)

factor theorem

a polynomial function f(x) has a factor of x-k if f(k)=0

upper bound

no sign change in quotient

lower bound

alternating signs

standard form of complex numbers

a+bi