# Quadratic Vocabulary for Algebra II

### By: Julia Ledbetter 3rd period

## Vertex

Definition: The point at which the axis of symmetry intersects a parabola.

## Axis of Symmetry

Definition: A line about which a quadratic function (parabola) is symmetric. The equation used to find the axis of symmetry is shown below.

## Maximum Value

Definition: The y-coordinate of the vertex of the quadratic function

f(x)=a^2 + bx + c, where a<0

## Minimum Value

Definition: The y-coordinate of the vertex of the quadratic function

f(x)=ax^2 + bx + c, where a>0

## Standard Form

Definition: A quadratic equation written in the form: ax^2 + bx+ c=0, where

*a*,*b*, and*c*are integers, and*a*cannot = 0This form is to help you find the y intercept.

## Vertex Form

Definition: A quadratic function in the form y= a(x-h)^2 + k, where (

*h,k*) is the vertex of the parabola and x=h is its axis of symmetry.This form is to help you find the vertex.

## Example: Writing Functions in Vertex Form

## Example: Graph Equations in Vertex Form

## Intercept Form

Definition: y=a(x-r1)(x-r2)

This form is to help you find the roots.

## Completing the Square

Definition: All quadratic equations can be solved using the Square Root method Property by manipulating the equation until one side is a perfect square, which is called "completing the square". You are changing the equation from

**standard form**to**vertex form**.Follow the Steps below to Complete the Square:

1. Put () around ax^2 + bx

2. Factor the a value from x^2 and x

3. Take 1/2 the middle term and square it

4. Add the number and it's opposite

5. Factor perfect square trinomial

6. Rewrite in the form y= a(x-h)^2 + k (which is vertex form)

## Example: Completing the Square

## Quadratic Formula

Definition: The solutions of a quadratic equation of the form is ax^2 + bx + c=0, where

*a*cannot equal 0, are given by the Quadratic Formula, which is shown below.## Example: Solving with Quadratic Formula

## Root (solution, x-intercept, zero)

Definition: The solutions of a quadratic equation. Also known as solutions, x-intercepts, and zeros.