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. Warm Ups Find the zeros of the function. Tuesday, October 27, 2015 Find the x-intercepts

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. 2 Tuesday, October 27, 2015 Essential Question: How do we use the square root property?

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. Vocabulary

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. 4 Key Concept 1.Isolate the radical. 2.Take the square root. 3.Simplify the radical.

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. 5 Example Solve the quadratic equation.

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. 6 Guided Practice Solve the quadratic equation.

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. 7 Guided Practice Solve the quadratic equation.

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. 8 Guided Practice Solve the quadratic equation.

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. Solve the equation. 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. Use h = -16t 2 + h 0 Height of the object after it has fallen # of seconds after the object is dropped Object’s initial height Key Concept

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. 11 6. The tallest building in the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground? Example

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. 7. A rescue helicopter hovers 68 feet above a jet ski in distress and drops a life raft. The height in feet of the raft above the water is given by h(t) = -16t 2 + 68. Determine how long it will take for the raft to hit the water after being dropped from the helicopter. Solution: The raft will hit the water when its height is 0 feet above the water. Solve h(t) = -16t 2 + 68 = 0. -16t 2 + 68 = 0 -16t 2 = - 68 The life raft will hit about 2.1 seconds after it is dropped. Ignore the - 2.1. WHY?

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. Model a dropped object with a quadratic function 8. Science Competition For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. How long does the container take to hit the ground? Use h = – 16t 2 + 50 0 = – 16t 2 + 50 – 50 = – 16t 2 50 16 = t 2 50 16 + = t 2 + 1.8 ≈ t Reject the negative solution, – 1.8, because time must be positive. The container will fall for about 1.8 seconds before it hits the ground.

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. 14