Chapter 6.3 Solving Quadratic Functions by Factoring Standard & Honors Algebra II Mr. Gilbert Chapter 6.3 Solving Quadratic Functions by Factoring Standard & Honors 11/30/2018

Agenda Warm up Homework Check your answers Applet Lesson 11/30/2018

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Solving Quadratic Functions by Factoring Example 1 Two Roots (4) Example 2 Double Root (3) Example 3 Greatest Common Factor (3) Example 4 Write an Equation Given Roots (3) 11/30/2018 Lesson 3 Contents

Solve the second equation. Solve by factoring. Original equation Add 4x to each side. Factor the binomial. Zero Product Property or Solve the second equation. Answer: The solution set is {0, –4}. 11/30/2018 Example 3-1a

Check Substitute 0 and –4 in for x in the original equation. 11/30/2018 Example 3-1a

Subtract 5x and 2 from each side. Solve by factoring. Original equation Subtract 5x and 2 from each side. Factor the trinomial. Zero Product Property or Solve each equation. Answer: The solution set is Check each solution. 11/30/2018 Example 3-1a

Solve each equation by factoring. a. Answer: {0, 3} Answer: 11/30/2018 Example 3-1b

Answer: The solution set is {3}. Solve by factoring. Original equation Add 9 to each side. Factor. Zero Product Property or Solve each equation. Answer: The solution set is {3}. 11/30/2018 Example 3-2a

Check The graph of the related function, intersects the x-axis only once. Since the zero of the function is 3, the solution of the related equation is 3. 11/30/2018 Example 3-2a

Solve by factoring. Answer: {–5} 11/30/2018 Example 3-2b

Multiple-Choice Test Item What is the positive solution of the equation ? B 5 C 6 D 7 Read the Test Item You are asked to find the positive solution of the given quadratic equation. This implies that the equation also has a solution that is not positive. Since a quadratic equation can either have one, two, or no solutions, we should expect this equation to have two solutions. 11/30/2018 Example 3-3a

Solve the Test Item Original equation Factor. Divide each side by 2. Zero Product Property Solve each equation. Both solutions, –3 and 7, are listed among the answer choices. However, the question asks for the positive solution, 7. Answer: D 11/30/2018 Example 3-3a

Multiple-Choice Test Item What is the positive solution of the equation ? B –5 C 2 D 6 Answer: C 11/30/2018 Example 3-3b

Write a quadratic equation with and 6 as its roots. Write the equation in the form where a, b, and c are integers. Write the pattern. Replace p with and q with 6. Simplify. 11/30/2018 Example 3-4a

Multiply each side by 3 so that b is an integer. Use FOIL. Multiply each side by 3 so that b is an integer. Answer: A quadratic equation with roots and 6 and integral coefficients is You can check this result by graphing the related function. 11/30/2018 Example 3-4a

Write a quadratic equation with and 5 as its roots. Write the equation in the form where a, b, and c are integers. Answer: 11/30/2018 Example 3-4b

Homework Review 11/30/2018

Homework - Honors See Syllabus 6.3 pp. 304: 14-40 even, 42-47 11/30/2018

Homework See Syllabus 6.3 pp. 304: 14 – 40 even, 42-45 11/30/2018