Reteach 5-6

Name
LESSON
5-6
Date
Class
Reteach
The Quadratic Formula
The Quadratic Formula is another way to find the roots of a quadratic
equation or the zeros of a quadratic function.
Find the zeros of f x x 2 6x 11.
Step 1 Set f x 0.
x 2 6x 11 0
Step 2 Write the Quadratic Formula.
b 2 4ac
_______________
x b
2a
Step 3 Substitute values for a, b, and c into the Quadratic Formula.
a 1, b 6, c 11
2
6 6 4 1 11 b 2 4ac ___________________________
_______________
x b
2a
2 1 Step 4 Simplify.
6 6 2 4 1 11 36 44 6
80
________
x ___________________________
6_____________
2
2
2 1
Step 5 Write in simplest form.
80 3 _____
4 5 3 2 16 5 3 ____
80 3 _________
________
x6
5
2
2
2
2
Remember to divide both terms of
the numerator by 2 to simplify.
Find the zeros of each function using the Quadratic Formula.
2
1. f x x x 1
2. f x x 2 6x 6
x 2 6x 6 0
x2 x 1 0
a
1
,b
1
,c
1
a
6 , c 6
b 2 4ac
______________
x b
2a
2
1 1 4 1 1 x _______________________________
2 1 6 兹 6 2 4 1 6 __________________________
x
2 1 兹 36 24
x 6_____________
2
兹1 4
____________
x 1
2
5
1
兹
________
x
2
a207c05-6_rt.indd 46
,b
b 2 4ac
______________
x b
2a
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
1
x 3 兹3
46
Holt Algebra 2
12/15/05 4:35:40 PM
Process Black
Name
LESSON
5-6
Date
Class
Reteach
The Quadratic Formula (continued)
The discriminant of ax 2 bx c 0 a 0 is b 2 4ac.
Use the discriminant to determine the number of roots of a quadratic equation. A quadratic
equation can have 2 real solutions, 1 real solution, or 2 complex solutions.
Find the type and number of solutions.
2x 2 5x 3
x 2 10x 25
3x 2 4x 2
Write the equation in
standard form:
Write the equation in
standard form:
Write the equation in
standard form:
2
2x 5x 3 0
2
x 10x 25 0
2
3x 4x 2 0
a 2, b 5, c 3
a 1, b 10, c 25
Evaluate the discriminant:
Evaluate the discriminant:
Evaluate the discriminant:
b 4ac
b 4ac
2
b 4ac
5 2 4 2 3 10 2 4 1 25 4 2
25 24
100 100
16 24
49
0
8
2
2
When b 4ac 0,
the equation has 2 real
solutions.
2
When b 4ac 0, the
equation has 1 real solution.
2
a 3, b 4, c 2
4 3 2 2
When b 4ac 0, the
equation has 2 complex
solutions.
Find the type and number of solutions for each equation.
3. x 2 12x 36
x 2 12x 36 0
a
1
,b
12 , c 36
b 2 4ac 4. x 2 4x 7
x 2 4x 7 0
a 1, b 4, c 7
b 2 4ac 0
Classify solutions:
1 real solution
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-6_rt.indd 47
12
Classify solutions:
2 complex solutions
47
5. x 2 7x 3
x 2 7x 3 0
a 1, b 7, c 3
b 2 4ac 37
Classify solutions:
2 real solutions
Holt Algebra 2
12/15/05 4:35:41 PM
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