Math Formulas: Algebra2/Trig H S1

Standard Form

Y=aX²+bX+c

Vertex Form

Y=a(X-p)²+k

Factored Form

Y=a(X-p)(X-q)

Slope Intercept Form (linear)

Y=mX+b

Standard form (linear)

c=aX+by

Point Slope Form (linear)

Y-y1=m(X-x1)

Intercept Form (Linear)

X/a+Y/b=1

Slope Formula

y2-y1/x2-x1

Perpendicular Slope

-b/a

Completing the square value

(b/2)²

Translations

-a(-bX+c)+d

Midpoint formula

(x1+x2/2),(y1+y2/2)

Vertical motion model

h(t)=-16+vo(t)+ho

Intermediate Value Theorem

a≠b; P(a) and P(b) opposite signs, a 0 in between

Polynomial checklist

1. EB:even vs odd + vs -

2. Zeros: at most n zeros

3. Multiplicity: cross or tangent, sign test intervals

4. Y-intercepts: evaluate F(0)

5. Turning points: at most n-1 turning points

6. additional points

Rational Zeros Theorem

+- p/q

Remainder Theorem

F(2)=21 then synthetic devision with 2 will have remainder 21

Irrational Zeros

If a-bi then a+bi

If a-sqrtb then a+sqrtb

Difference of Cubes

X³-a³=(X-b)(X²-bX+b²)

Rational Equations

1. Vertical Asymptotes: factor denominators (exclude common factors)

2. End Behavior Asymptotes:

   1. m=n then y=a

   2. m>n then quotient of num/den

   3. m<n then y=0

3. Holes: common factors. If num multiplicity>den multiplicity then hole is on x-axis

4. x-intercepts: factor numerator (exclude common factors)

5. y-intercepts: set X to 0 and simplify

6. extra points

The Simple Interest Formula

I=Prt

The Future Value Interest FormulaA'

A=P+Prt

Compound Interest

A=P(1+r/n)^nt

Compound Continuously

P(t)=Pe^rt

Exponential Growth

y=a(1+b)^x

Exponential Decay

y=a(1-b)^x

Doubling Formula

y=a(2)^t/d

Halving Formula

y=a(1/2)^t

Change Base

log(b)c=log(a)c/log(a)b