# Quadratics

### By: Sajithan Sethukavalar

## Linear vs. Non-Linear

## Vertex Form

y=a(x-h)²+k

In quadratics vertex form is only one the forms of a quadratic equation. On this site you will be learning about axis of symmetry, vertex, the step pattern as learned above, how to find the x intercept, transformations and how to graph a parabola using the vertex form equation.

## Step Pattern

The "x" and new "y" values are the points making the parabola.

## Terms

## Optimal Value (Min and Max Value)

- It is the value of the y in the vertex point
- Minimum value is when graph opens up
- Maximum value is when graph opens down

## Axis of Symmetry

- It is a line divides the parabola in half making it the same on each side
- It is the "h" in the equation and is always opposite of what it appears in the bracket.

## Vertex (H,K)

- The vertex is the highest point of parabola
- It is the point where the graph changes direction
- The vertex can be found in the equation in the form of "h" and "k"

## Tranformations

## "a"

The "a" value determines the opening and vertical stretch or compression of the parabola

**Shape:**

- If the value of "a" is more than one then the parabola is vertically stretched
- If the value of "a" is less than one then the parabola is vertically compressed

**Orientation:**

- If the value of "a" is negative the parabola opens down
- If the value of "a" is positive the parabola opens up

## "h"

The "h" value determines if the parabola moves right or left

**Orientation:**

- If the "h" value is negative the parabola moves to the right
- If the "h" value is positive the parabola moves to the left

## "k"

The "k" value determine whether the parabola is moved up or down.

**Orientation:**

- If the "k" value is positive the parabola is moved up.
- If the "k" value is negative the parabola is moved down

## Graphing

- The way I like to use is to graph a parabola using the vertex form, you can start by finding and plotting the vertex. Then you multiply using the step pattern and plot the points, then connect them.
- The other way is mapping notation.It is mainly going from y=x² to y=a(x-h)² +k. This is done by making a chart with "x" values then subbing it into the equation making points as shown below.

Graphing Quadratic Functions Using Transformations