The Quadratic Formula

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 07:26 PM UTC

OBJECTIVES:
1. Derive the quadratic formula.
2. Solve quadratic equations using the quadratic formula.
3. Use the discriminant to determine the number and type of solutions.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.2 - 1

2. Chapter 10
Quadratic Equations,
Inequalities,
and Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.2 - 2

3. 10.2
The Quadratic Formula
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 10.2 - 3

4. 10.2 The Quadratic Formula
Objectives
1. Derive the quadratic formula.
2. Solve quadratic equations using the quadratic
formula.
3. Use the discriminant to determine the number
and type of solutions.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 4

5. 10.2 The Quadratic Formula
Derive the Quadratic Formula
We can use the method of completing the square to solve any
quadratic equation. However, completing the square can
become tedious and time consuming. In this section, we begin
with the general quadratic equation
By applying the method of completing the square to this
general equation, we can develop a formula for finding the
solution of any specific quadratic equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 5

6. 10.2 The Quadratic Formula
Derive the Quadratic Formula
Applying the Method of Completing the Square
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 6

7. 10.2 The Quadratic Formula
Derive the Quadratic Formula
Applying the Method of Completing the Square Cont’d.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 7

8. 10.2 The Quadratic Formula
Derive the Quadratic Formula
Applying the Method of Completing the Square Cont’d.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 8

9. 10.2 The Quadratic Formula
Stating and Applying the Quadratic Formula
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 9

10. 10.2 The Quadratic Formula
Stating and Applying the Quadratic Formula
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 10

11. 10.2 The Quadratic Formula
Statement of the Quadratic Formula
You should always check each
solution in the original equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 11

12. 10.2 The Quadratic Formula
Statement of the Quadratic Formula
Always try factoring first. If
factoring is difficult or impossible,
use the quadratic equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 12

13. 10.2 The Quadratic Formula
Using Quadratic Formula (Irrational Solutions)
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14. 10.2 The Quadratic Formula
Using Quadratic Formula (Irrational Solutions)
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 14

15. 10.2 The Quadratic Formula
Simplifying the Results Using the Quadratic Formula
Be sure to factor first; then
divide out the common factor.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 15

19. 10.2 The Quadratic Formula
What Information the Discriminant Predicts
If the discriminant is a perfect square (including 0), then the
equation can be factored; otherwise, the quadratic formula
should be used.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 19

20. 10.2 The Quadratic Formula
What Information the Discriminant Predicts
The value of the discriminant
is –44 and the equation has
two nonreal complex solutions
and is best solved with the
quadratic formula.
Because the discriminant is 0,
there is only one rational
solution, and the equation can
be solved by factoring.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 20

21. 10.2 The Quadratic Formula
What Information the Discriminant Predicts
The discriminant is a perfect
square so there will be two
rational solutions and the
equation can be solved by
factoring.
The value of the discriminant
is 109 and the equation has
two irrational solutions and is
best solved with the quadratic
formula.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.2 - 21

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