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Warm Up

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!

2

• 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: