The document contains two examples involving quadratic equations modeling the motion of objects in the air. The first part reviews properties of the quadratic function y = x^2 - 2x - 8, including its x-intercepts, axis of symmetry and vertex, and whether its graph is a function. The second example gives the quadratic equation d = rt - 16t^2 that models height d of an object over time t, and asks questions about a ball thrown with speed 64 feet/second. The third example asks similar questions about the motion of a basketball player jumping with initial speed 16 feet/second.

1. Quadratic Functions Review y = x 2 – 2x - 8 a) Find the x-intercepts b) Find the axis of symmetry and vertex. Is the vertex a maximum or minimum? c) Sketch the graph d) Is the graph a function? Why or why not?

2. When an object is thrown into the air, the equation: d = rt – 16t 2 can be use to represent its motion where d = height of object above point of release, r = initial upward speed, and t = time For a ball thrown into the air with an initial speed of 64 feet per second, the equation is _______________ a) How long is the ball in the air? b) What is the maximum height that the ball reached? c) How long did it take the ball to reach its maximum height? Example 1