Quadratic Formula

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𝐹𝑜𝑖𝑙 (𝑥 + 3)(2𝑥 + 2)

Solving Quadratic Equations by the Quadratic Formula

Refresh • Remember the GENERAL FORM of a quadratic equation is 𝒚 = 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 Where a,b and c are numbers.

Practice • • • • • Write in general form and identify a,b and c.

𝑥 2 − 5𝑥 = −3 We need to add 3 to both sides 𝑥 2 − 5𝑥 + 3 a= 1 b= -5 c= 3

You try • 3𝑥 2 = 4𝑥 − 5 • Answer: 3𝑥 2 − 4𝑥 + 5 • a=3 b= -4 c=5

Try again: put in general form • 𝑥 + 2 𝑥 − 2 = 6 • Answer: 𝑥 2 − 10 • a=1 b=0 c= -10

What does it mean to “solve”?

• When you are asked to “solve” a quadratic, it is asking you to find the roots.

THE QUADRATIC FORMULA

x



b

2  4

ac

2

a

What do we do with it?

Step 1: Put in General form, and set equation = to 0. Step 2: Identify a, b, and c in your quadratic

𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄

.

Step 3: Substitute a.b and c into the quadratic formula.

Example • 𝑦 = 𝑥 2 + 4𝑥 + 3 • a=1. b=4. c=3 • • 𝑥 = −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥 = −4± 4 2 −4∙1∙3 2∙1

Example 1 continued • 𝑥 = −4± 4 2 • 𝑥 = −4+2 2 𝑎𝑛𝑑 𝑥 = −4−2 2 • x=-1 and x=-3

WHY USE THE QUADRATIC FORMULA?

The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it.

Example 2 • 𝑥 2 + 2𝑥 = 63 Answer: −9 𝑎𝑛𝑑 7

Example 3: You try 𝑥 2 + 8𝑥 − 84 • Answer: 6 , -14

Example 4: you try again!

𝑥

2

− 5𝑥 = 24

• Answer: -3, 8

You try! Start with 1 and 4, then go on to the others. 1.

x

2 2.

x

2 3.

x

2 4.

x

2 5. 3

x

  2

x

8

x

 5

x

 7

x

2  5

x

 63  84  24  13     1.

3.

0 4.

0 2 5.

        9, 7  3,8    

i

6

i

3   47  

• • • 9.7

1: all 3: a and b. Homework:

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