# Quadratic Relationships Website

### Unit 3: Standard Form

## Introduction

## Learning Goals

- I am able to use the quadratic formula in a quadratic equation.
- I am able to use the standard form equation, to complete the square, and graph the parabola
- I am able to find the x-intercepts of the equation, by using the quadratic formula.
- I am able to find the vertex of the equation, by completing the square.
- I am able to graph the x-intercepts and the vertex, then draw the parabola.

## Properties

## y=ax^2+bx+c

"c" value: represents the y-intercept

## Quadratic Formula

The quadratic equation is used when you are given a standard form equation and are asked to find out the x intercepts.

When asked to find out how many solutions(x-intercepts) there are you can use a simple equation to find out the number of solutions.

## For Example

## Discriminant

The Discriminant adapts the formula that is inside the square root of the Quadratic Formula (b^2-4ac). The Discriminant helps us find out how many solutions the given quadratic equation will have, without us solving the entire equation with the Quadratic Formula. If the value of “** d**” is less than 0, so if it’s a negative, there will be no solutions. If the value of

**is greater than 0, there will be 2 solutions and if the value of**

*d***is 0, there will be 1 solution. So to sum up the Discriminant:**

*d*D<0- no solutions

D>0- 2 solutions

D=0- 1 solution

## Graphing Standard Form

- Find the x-intercepts of the equation with the quadratic formula
- Find the vertex by completing the square
- Graph x intercepts
- Graph vertex
- Draw parabola

## Completing the Square

To complete the square, divide *b *by two then square the quotient. Then, if *a isn't *1, add and subtract that product to the standard form equation. If *a *were 1, add the negative value of the product. Add the negative value and *c* value together after multiplying it with *a *if *a *does not equal 1. Put everything with the exception of the *c* value in brackets and use perfect squares method to solve by factoring. Next, put the factored part and add the *c* value. The result will be that your successfully converted it into vertex form.