Warm Up
 ( + 3)(2 + 2)
Solving Quadratic
Equations by the
Quadratic Formula
Refresh
• Remember the GENERAL FORM of a quadratic
equation is  =  +  + 
Where a,b and c are numbers.
Practice
•
•
•
•
•
Write in general form and identify a,b and c.
 2 − 5 = −3
We need to add 3 to both sides
 2 − 5 + 3
a= 1 b= -5 c= 3
You try
• 3 2 = 4 − 5
• Answer: 3 2 − 4 + 5
• a=3 b= -4 c=5
Try again: put in general form
• +2 −2 =6
• Answer:  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
b  b  4ac
x
2a
2
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  +  + .
Step 3: Substitute a.b and c
into the quadratic formula.
Example
•  =  2 + 4 + 3
• a=1. b=4. c=3
• =
−± 2 −4
2
• =
−4± 42 −4∙1∙3
2∙1
Example 1 continued
•=
−4± 4
2
•=
−4+2
2
  =
• x=-1 and x=-3
−4−2
2
WHY USE THE
QUADRATIC FORMULA?
The quadratic formula allows you to solve
ANY quadratic equation, even if you
cannot factor it.
Example 2
•
2

+ 2 = 63
Answer: −9  7
Example 3: You try
2

• Answer: 6 , -14
+ 8 − 84
Example 4: you try again!
2
 − 5 = 24
• Answer: -3, 8
You try!
Start with 1 and 4,
then go on to the others.
1. x  2 x  63  0
2
2. x  8 x  84  0
2
3. x  5 x  24  0
2
4. x  7 x  13  0
2
5. 3 x 2 5 x  6  0
1.  9, 7 
2.(6, 14)
3.  3,8 
 7  i 3 
4. 

2


 5  i 47 
5. 

6


Homework:
• 9.7
• 1: all
• 3: a and b.
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Quadratic Formula

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