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

63

1.
 
9, 7
0

2.
3.
4. x x x
5. 3
2
2
2 x



2
8
5
7

5 x x x x



84
24
13
6



0
3.
2
5.

0





3,8
 
 

6 i i
3
47





• 9.7
• 1: all
• 3: a and b.
Homework: