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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

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Chapter P: Prerequisite Information

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  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

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