# Standard Form

### By: Jasmeen Mann

## Learning Goals

1. What is factoring?

2. What is completing the square?

3. The process to change a standard form to vertex form.

4. Know when the points are maximum or minimum.

5. Formula for quadratic relations of the form.

## Standard form to vertex form

y=ax^2+bx+c which is standard form

y= a(x-h)^2+k which is vertex form

## Completing the Square to turn to Vertex Form

Completing a square means to make an equation a perfect square trinomial. In order to do so, there are a few simple steps to follow:

## Step of completing a square

First, put the first 2 terms(x^2 and ) into parentheses. Remember that c goes outside the parentheses. Next, take out a greatest common factor if possible. In the example to the right, a greatest common factor of -9 can be taken out. Keep in mind don't count.

Example: -9x^2+36+8

=(-9x^2-36)+8

=-9(x^2+4)+8

-9(x^2+4x)+8

4/2=2

2*2

4

-9(x^2+4x+4-4)+8

-9(x^2+4x+4-4)+8

=-9(x^2+4x+4)+36+8

=-9(x^2+4x+4)+44

-9(x^2+4x+4)+44

=-9(x+2)^2+44

The final answer should be in vertex form.

-9(x+2)^2+44

## Using the Quadratic Formula

The Quadratic formula is used when a cettain quardratic cannot be factored. This formula was developed by completing the square and solving the qudratic ax^2+bx+c=0.

The formula tells us that x=

## Number of Solutions and the Discriminant

Discriminant (D): (b^2-4ac)

When D<0, then their would be no solutions and no x-intercepts.

When D>0, then their would be two soultions.

When D=0, then their would be only one soultions.

## Graph

Solving Quadratic Equations by Graphing

## Word Problems

More Word Problems Using Quadratic Equations - Example 1