# Quadratics

## Key features of Quadratic Relations (vertex, AOS, zeros, optimal value)

The graph of a quadratic relation is called parabola. A parabola has some key important features.

Axis of Symmetry: A vertical line that divides the parabola in half

Vertex: The highest or lowest point of a parabola

Zeros: The point at which the parabola intersects the x-axis

Optimal value: The maxim or minimum value

## Quadratic Relations and finite differences

Finite differences determine if the relation is Linier. Quadratic or Neither.

## Transformations of Quadratics Y=a(x-h)+k

Y=a(x-h)+k is the equation to a parabola.

A: If positive parabola opening up, if negative parabola opening down

H: The X-intercept of the vertex. If negative parabola will move to the left, If positive the Parabola will move to the right

K: The Y-intercept of the vertex

## Finding X and Y intercepts

To find X intercept you must sub 0 In for Y

To find Y intercept you must sub 0 in for X

Example: X=3y+4

X=4(0)+4

X=4

0=3y+4

-4=4y

-1=y

## Multiplying Binomials and Special Products

Example 1: (x+3)^2=(x+3)(x+3) Example 2: (x+3)(x-3)=x^2-3x+3x-9

=x^2+3x+3x+9 =x^2-9

=x^2+6x+9

## Factoring simple trinomials

>Ex1: 5y-30 >Ex2: 2x^3-6x

> 5 is the only thing common in this equation >2x is common in this equation

> divide the equation by 5 >divide the equation by 2x

>5(y-6) >2x(x^2-3)

## Factoring complex trinomials

Ex1: 4x^4-6x^3+2x^2+2x

>The whole equation divides by 2x

>2x(2x^3-3x^2+x+1)