1. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Warm Ups Solve the equations. Sunday, December 20, 2015

2. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

3. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. 3 Sunday, December 20, 2015 Essential Question: How do we find the zeros of a quadratic equation? Lesson 3.4

4. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. 4 Solutions of a quadratic equation or function. If y = f (x) is a quadratic function and a is a real number then the following statements are equivalent. 1. x = a is a zero of f. 2. x = a is a root of f. 3. x = a is a solution of the quadratic equation f (x) = 0. 4. (x – a) is a factor of the quadratic f (x). 5. (a, 0) is an x-intercept of the graph of y = f (x).

5. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. 5 +3 -28 +7 -4 1. or Apply the Zero Product Property. Solve both equations. The solutions are -7 and 4. Factor. Find the zeros of the quadratic function. Substitute zero for y.

6. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. 6 -10 +24 -6 -4 Find the zeros of the function. 2. Substitute y = 0. or Apply the Zero Product Property. Solve both equations. The zeros are 6 and 4. Factor. Guided Practice

7. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. 7 -13 +12 -12 Find the zeros of the function. 3. Substitute y = 0. or Apply the Zero Product Property. Solve both equations. The zeros are 12 and 1. Factor. Guided Practice

8. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function. 4. The zeros are 0 and 11. Guided Practice

9. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function. 5. Guided Practice The zeros are 0 and -15.

10. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function. 6. Guided Practice

11. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function. 7. Guided Practice

12. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function. 8. Guided Practice

13. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function, then write the equation. 9. Guided Practice

14. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function, then write the equation. 10. Guided Practice

15. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function, then write the equation. 11. Guided Practice

16. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula. Find the zeros of the function, then write the equation. 12. Guided Practice