1. Sullivan Algebra and Trigonometry: Section 4.1 Objectives Graph a Quadratic Function Using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph a Quadratic Function Using the Vertex, Axis of Symmetry, and Intercepts Use a Graphing Utility to Find the Quadratic Function of Best Fit

2. A quadratic function is a function of the form: where a, b, and c are real numbers and a 0. The domain of a quadratic function consists of all real numbers. The graph of a quadratic function is called a parabola.

3. Graphs of a quadratic function f(x) = ax 2 + bx + c, a 0 a > 0 Opens up Vertex is lowest point Axis of symmetry a < 0 Opens down Vertex is highest point Axis of symmetry

4. Graph the function fxxx()  281 2 Find the vertex and axis of symmetry. First, rewrite the function by completing the square

5. Now, graph the function using the transformations discussed in Chapter 3. (0,0) (2,4) (0,0) (2, -8)

6. (2, 0) (4, -8) (2, 7) (4, -1) Vertex : (2,7)

7. Characteristics of the Quadratic Function Parabola opens up if a > 0. Parabola opens down if a < 0.

8. Given the function, determine whether the graph opens upward or downward. Find the vertex, axis of symmetry, the x- intercepts, and the y-intercept. fxxx()  2125 2 x-coord. of vertex: y-coord. of vertex: Axis of symmetry: x b a    2 3 Vertex: (-3, -13)

9. fxxx()  2125 2 y-intercepts: f(0) = 5; so the y-intercept is (0,5) x-intercepts: Solve the equation = 0 fxxx()  2125 2 The x-intercepts are approximately (-5.6,0) and (-.45,0) Summary: Parabola opens up Vertex (-3, -13) y-intercept: (0,5) x-intercepts: (-0.45, 0) and (-5.55,0)

10. Now, graph the function using the information found in the previous steps. Vertex: (-3, -13) (-5.55, 0)(-0.45, 0) (0, 5)

11. Suppose you throw a ball straight up and record the height of the ball in 0.5 second intervals and obtain the following data:

12. Use a graphing utility to complete the following: a.) Draw a scatter diagram of the data. b.) Find the quadratic function of best fit. c.) Draw the quadratic function of best fit on the scatter diagram.