Algebra II Mr Gilbert Chapter 6 3 Solving

Algebra II Mr. Gilbert Chapter 6. 3 Solving Quadratic Functions by Factoring Standard & Honors 1/31/2022 1

Agenda Warm up u Homework u – Check your answers Applet u Lesson u 1/31/2022 2

1/31/2022 Click the mouse button 3 or press the Space Bar to display the answers.

1/31/2022 4

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) 1/31/2022 5

Solve by factoring. Original equation Add 4 x to each side. Factor the binomial. or Zero Product Property Solve the second equation. Answer: The solution set is {0, – 4}. 1/31/2022 6

Check Substitute 0 and – 4 in for x in the original equation. 1/31/2022 7

Solve by factoring. Original equation Subtract 5 x and 2 from each side. Factor the trinomial. or Zero Product Property Solve each equation. Answer: The solution set is 1/31/2022 Check each solution. 8

Solve each equation by factoring. a. Answer: {0, 3} b. Answer: 1/31/2022 9

Solve by factoring. Original equation Add 9 to each side. Factor. Zero Product Property or Solve each equation. Answer: The solution set is {3}. 1/31/2022 10

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. 1/31/2022 11

Solve by factoring. Answer: {– 5} 1/31/2022 12

Multiple-Choice Test Item What is the positive solution of the equation ? A – 3 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. 1/31/2022 13

Solve the Test Item Original equation Factor. Divide each side by 2. Factor. or 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 1/31/2022 14

Multiple-Choice Test Item What is the positive solution of the equation ? B – 5 A 5 C 2 D 6 Answer: C 1/31/2022 15

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. 1/31/2022 16

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. 1/31/2022 17

Write a quadratic equation with and 5 as its roots. Write the equation in the form where a, b, and c are integers. Answer: 1/31/2022 18

Homework Review 1/31/2022 19

Homework - Honors See Syllabus 6. 3 pp. 304: 14 -40 even, 42 -47 1/31/2022 20

Homework See Syllabus 6. 3 pp. 304: 14 – 40 even, 42 -45 1/31/2022 21