IM Alg1.7.24 Lesson: Using Quadratic Equations to Model Situations and Solve Problems

and

and

Solve this equation: . Show your reasoning.

The function , defined by , models the height of a diver above the water (in meters), seconds after the diver leaves the board. For each question, explain how you know. How high above the water is the diving board?

When does the diver hit the water?

At what point during her descent toward the water is the diver at the same height as the diving board?

When does the diver reach the maximum height of the dive?

What is the maximum height the diver reaches during the dive?

Another diver jumps off a platform, rather than a springboard. The platform is also 7.5 meters above the water, but this diver hits the water after about 1.5 seconds. Write an equation that would approximately model her height over the water, , in meters, seconds after she has left the platform. Include the term , which accounts for the effect of gravity.

Here are graphs of a linear function and a quadratic function. The quadratic function is defined by the expression . Find the coordinates of , and without using graphing technology. Show your reasoning.