# Quadratics Standard Form.

### All you need for Math.

## Learning Goals.

By the end I will be able to:

1) Complete the Square

2) Use the quadratic formula, to get the x-intercepts

3) Do revenue questions

4) Find Vertex and Max/Min value from an equation

1) Complete the Square

2) Use the quadratic formula, to get the x-intercepts

3) Do revenue questions

4) Find Vertex and Max/Min value from an equation

## Summary of the unit

In this unit you will learn how to Complete the square, use the Quadratic Formula, do revenue questions and you will learn how to find the Max or Minimum value and the vertex. Then you will learn what each variable does and learn how to do a word problem.

## Meaning of each variable in 𝑦=𝑎𝑥^2+𝑏𝑥+𝑐

**1st E.x. y=2x^2 + 1x - 19.**The a value tells us that this equation is stretching by a factor of 2 and opening upwards. The x variables can be time or distance in an equation. The c variable tells us the y intercept ant the maximum or minimum value, which is -19.

**2nd E.x. y=-2x^2 + 1x + 56.**The a value tells us that this equation is stretching by a factor of 2 and opening downwards. The x variables can be time or distance in an equation. The c variable tells us the y intercept ant the maximum or minimum value, which is 56.

**3rd E.x. y= 0.5x^2 +1x + 3.8.**In this equation, a tells us that it is vertically compressing by a factor of 0.5. The x variables can be time or distance in an equation. The c variable tells us the y intercept ant the maximum or minimum value, which is 3.8.

## Types of standard form questions

## Completing the square

How to complete the square:

E.x. there is an equation: y= (x+8x)+2

First take 8 then divide it by 2= 4. then square it, which equals 16.

Then put 16 into the equation which makes y= (x+8x+16-16)+2. YOU MUST PUT A NEGATIVE NUMBER AS WELL.

Take y= (x+8x+16-16)+2 and take -16 outside and solve.

This will make it now y= (x+8x+16)-14.

Now put in 4 in place of 8x and erase 16 and put a ^2.

Your answer should be: y= (x + 4)^2 -14

E.x. there is an equation: y= (x+8x)+2

First take 8 then divide it by 2= 4. then square it, which equals 16.

Then put 16 into the equation which makes y= (x+8x+16-16)+2. YOU MUST PUT A NEGATIVE NUMBER AS WELL.

Take y= (x+8x+16-16)+2 and take -16 outside and solve.

This will make it now y= (x+8x+16)-14.

Now put in 4 in place of 8x and erase 16 and put a ^2.

Your answer should be: y= (x + 4)^2 -14

## Quadratic Formula

How to do quadratic formula questions: look at the image

## Revenue questions

How to do revenue questions: look at the image

Writing Linear Equations: Standard Form

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