6.2 Quadratic formulas

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• Middelbare school
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Quadratic Formulas

Today you will learn:

What are quadratic formulas and how can I use them? 

Yesterday you learned

Squares

          7² = 49

Squares of negative numbers

          -7² = -49

          (-7)² = 49

Square roots

          √49 = 7

Calculate:
6² + (-3)²

1. -45
2. 27
3. 45
4. -27

Calculate:
-5 * -8²

1. 78400
2. 320
3. -320
4. 169

Calculate:
-1 - 5 * (-2)²

1. -21
2. -24
3. 19
4. 20

Calculate:
√16 - √49

1. -5.7
2. 3
3. 28
4. -3

Calculate:
√4 * √1 * √0

1. 0
2. 1
3. 2
4. Not possible

Quadratic Formulas

Formulas with letters:

          y = -2x + 8

Quadratic formulas:

          y = -2x² + 8

An example

This row of shapes can be extended. 

How many dots does shape 5 consist of? 

And shape 6? 

And shape 10?

An example

-What is the number of the shape with 144 dots?

-How do you calculate the number of dots in a shape with number n?

-What is the formula for this row?

An example

What is the formula for this row?

a = n²

This is an example of a quadratic formula.

Using quadratic formulas

a = n²

What is a if you have n = 3?

And if n = 20?

And if n = -5?

Using quadratic formulas

a = n²

What is a if you have n = 3?

a = 3² = 3*3 = 9

And if n = 20?

a = 20² = 20*20 = 400

And if n = -5?

a = (-5)² = -5 * -5 = 25

Formula: a = n²
Calculate a when n = 8

1. 8
2. 16
3. 64
4. 640

Formula: y = 3x² - 6
Calculate y when x = 4

1. 42
2. 48
3. 54
4. 138

Formula: y = 3x² - 6
Calculate y when x = -5

1. -81
2. 81
3. -69
4. 69

Formula: y = (x+5)²
Calculate y when x = 3

1. 28
2. 36
3. 64
4. 225

Formula: y = (x+5)²
Calculate y when x = -9

1. -16
2. 16
3. 45
4. -45

Now you know about Quadratic formulas!

 

Homework today: 3-14 

Homework Thursday: 15-24, NOT 17, 20