1. 1 What you will learn 1. How to create a quadratic function given a set of points. 2. How to develop a quadratic model for sample data.

2. Objective: 5.8 Determining a Quadratic Function 2 Writing an Equation in Vertex Form  Write a quadratic function for the parabola shown. Vertex: 2, -3 Point: 4, 1 Use: y = a(x – h) 2 + k

3. Objective: 5.8 Determining a Quadratic Function 3 You Try Write a quadratic function for the parabola shown. Vertex: (-2, 1) Point: (1, -1) Use: y = a(x – h) 2 + k

4. Objective: 5.8 Determining a Quadratic Function 4 Writing a Quadratic Function in Intercept Form Write a quadratic function for the parabola shown. Intercepts (-2,0) (3, 0) Point: (-1,2) Use: y=a(x – p)(x – q)

5. Objective: 5.8 Determining a Quadratic Function 5 You Try Write a quadratic function for the parabola shown. Intercepts: (1,0) (4,0) Additional point: (2, -6) Use: y=a(x - p)(x – q)

6. Objective: 5.8 Determining a Quadratic Function 6 Writing an Equation in Standard Form  It can be done but…

7. Objective: 5.8 Determining a Quadratic Function 7 Modeling Real-World Data The table shows the distance (in meters) traveled by a baseball hit at various angles and with a backspin. Find a quadratic equation that gives the distance a ball will travel given the angle it is hit. angle 10 o 15 o 30 o 36 o 42 o 45 o 48 o 54 o 60 o Dist. 61.283.0 130.4139.4 143.2142.7140.7132.8119.7

8. Objective: 5.8 Determining a Quadratic Function 8 Homework  Homework: page 309, 7-9 all, 10, 12, 17, 20-22 even, 35