1. Copyright © 2011 Pearson, Inc. P.5 Solving Equations Graphically, Numerically and Algebraically

2. Copyright © 2011 Pearson, Inc. Slide P.5 - 2 What you’ll learn about Solving Equations Graphically Solving Quadratic Equations Approximating Solutions of Equations Graphically Approximating Solutions of Equations Numerically with Tables Solving Equations by Finding Intersections … and why These basic techniques are involved in using a graphing utility to solve equations in this textbook.

3. Copyright © 2011 Pearson, Inc. Slide P.5 - 3 Example Solving by Finding x- Intercepts

4. Copyright © 2011 Pearson, Inc. Slide P.5 - 4 Solution

5. Copyright © 2011 Pearson, Inc. Slide P.5 - 5 Zero Factor Property Let a and b be real numbers. If ab = 0, then a = 0 or b = 0.

6. Copyright © 2011 Pearson, Inc. Slide P.5 - 6 Quadratic Equation in x A quadratic equation in x is one that can be written in the form ax 2 + bx + c = 0, where a, b, and c are real numbers with a ≠ 0.

7. Copyright © 2011 Pearson, Inc. Slide P.5 - 7 Completing the Square

8. Copyright © 2011 Pearson, Inc. Slide P.5 - 8 Quadratic Formula

9. Copyright © 2011 Pearson, Inc. Slide P.5 - 9 Example Solving Using the Quadratic Formula

10. Copyright © 2011 Pearson, Inc. Slide P.5 - 10 Solution

11. Copyright © 2011 Pearson, Inc. Slide P.5 - 11 Solving Quadratic Equations Algebraically These are four basic ways to solve quadratic equations algebraically. 1. Factoring 2. Extracting Square Roots 3. Completing the Square 4. Using the Quadratic Formula

12. Copyright © 2011 Pearson, Inc. Slide P.5 - 12 Agreement about Approximate Solutions For applications, round to a value that is reasonable for the context of the problem. For all others round to two decimal places unless directed otherwise.

13. Copyright © 2011 Pearson, Inc. Slide P.5 - 13 Example Solving by Finding Intersections

14. Copyright © 2011 Pearson, Inc. Slide P.5 - 14 Solution

15. Copyright © 2011 Pearson, Inc. Slide P.5 - 15 Quick Review

16. Copyright © 2011 Pearson, Inc. Slide P.5 - 16 Quick Review Solutions