1 / 15

Chapter P: Prerequisite Information

Chapter P: Prerequisite Information. Section P-5: Solving Equations Graphically, Numerically, and Algebraically. Objectives. You will learn about: Solving equations graphically Solving quadratic equations Approximating solutions of equations graphically

ingrid-franks
Download Presentation

Chapter P: Prerequisite Information

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter P:Prerequisite Information Section P-5: Solving Equations Graphically, Numerically, and Algebraically

  2. Objectives • You will 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 • Why: • These basic techniques are involved in using a graphing utility to solve equations

  3. Vocabulary • Quadratic equation in x • Completing the square • Quadratic formula • Point of intersection • Discriminant

  4. Example 1:Solving by Finding x-intercepts • Solve the equation 2x2 – 3x – 2 = 0. • Solve graphically using the trace key on your calculator. • Check your work algebraically.

  5. Zero Factor Property • Let a and b be real numbers. • If ab = 0, then either a = 0 or b = 0

  6. Quadratic Equation in x • A quadratic equation in x is one that can be written in the form: • ax2 + bx + c = 0 • where a, b, and c are real numbers and a ≠ 0

  7. Example 2:Solve by extracting square roots • Solve (2x – 1)2 = 9 algebraically.

  8. Completing the Square • To solve ax2 + bx + c = 0 by completing the square, add (b/2)2 to both sides of the equation and factor the left side of the new equation.

  9. Example 3:Solve by Completing the Square • Solve 4x2 - 20x + 17 = 0 by completing the square.

  10. Quadratic Formula • The solutions of the quadratic equation ax2 + bx + c = 0 where a ≠ 0 are given by the quadratic formula:

  11. Example 4:Solve using the quadratic formula • Solve the equation 3x2 – 6x = 5

  12. Solving Quadratic Equations Algebraically • There are four basic ways to solve quadratic equations algebraically: • Factoring • Extracting square roots • Completing the square • Using the quadratic formula

  13. Examples 5 and 6:Solve Graphically and Using Tables • Solve the equation x3 – x – 1 = 0

  14. Agreement About Approximate Solutions: • For approximations, round to a value that is reasonable for the context of the problem. For all others, round to two decimal places unless directed otherwise.

  15. Example 7:Solve by Finding Intersections • Solve the equation |2x – 1|= 6 • First graphically • Check algebraically

More Related