# Math Formulas and Concepts

## 15 terms

### Distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

### midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

(x-h)²-(y-k)²=r²

(h,k)

### slope intercept form

y=mx+b (m=Slope, b=Y-intercept)

### Point Slope

y-y1=m(x-x1)

x = -b ± √(b² - 4ac)/2a

### linear shifts

ƒ(x) = c >0/
ƒ(x)+c ƒ(x) Shifted c units up/
ƒ(x)-c ƒ(x) Shifted c units down/
ƒ(x+c) ƒ(x) Shifted c united to the left/
ƒ(x-c) ƒ(x) Shifted c units to the right/

### Combination of functions

(f+g)(x) = f(x) + g(x)/
(f-g)(x) = f(x) - g(x)/
(f•g)(x) = f(x) • g(x)/
(f÷g)(x) = f(x) ÷ g(x), g(x)≠0/

### Vertical Elongation and Compression

C•ƒ(x)/
if C>1 Vertical Eongation of the graph ƒ(x)/
if 0<C<1 Vertical Compression of the Graph ƒ(x)/
If C=-1 Reflection about the x-axis/

### Vertical and Horizontal, Elongation and Compression

Vertical Elongation=Horizontal Compression Vertical Compression = Horizontal Elongation

### Graphing Polynomial Functions

1. Find Zero's/
2. Multiplicity/
a. Even multiplicity makes graph bounce
b. Odd multiplicity makes graph pass through
3. Y-Intercept, set x=0/
4. End Behavior (number of total x's)/
a. x→ ∞, y→ ?
b. x→ -∞, y→ ?

### The Division Algorithm

P(x)÷D(x) = Q(x) + R(x)/D(x)

### Graphing Rational Functions

1. Vertical Asymptote (and Holes if any)/
2. Horizontal Asymptote (and if graph crosses) 3./ Slant Asymptote (if any)/
4. Find x and y intercepts/