IM Alg1.6.14 Lesson: Graphs That Represent Situations

The height in inches of a frog's jump is modeled by the equation  where the time, , after it jumped is measured in seconds. Find  and . What do these values mean in terms of the frog’s jump?

How much time after it jumped did the frog reach the maximum height? Explain how you know.

The equation  represents the height of a pumpkin that is catapulted up in the air as a function of time, , in seconds. The height is measured in meters above ground. The pumpkin is shot up at a vertical velocity of 23.7 meters per second. Without writing anything down, consider these questions:

• What do you think the 2 in the equation tells us in this situation? What about the ?

• If we graph the equation, will the graph open upward or downward? Why?

• Where do you think the vertical intercept would be?

• What about the horizontal intercepts?

Identify the vertical and horizontal intercepts, and the vertex of the graph. Explain what each point means in this situation.

What approximate vertical velocity would this pumpkin need for it stay in the air for about 10 seconds? (Assume that it is still shot from 2 meters in the air and that the effect of gravity pulling it down is the same.)

Here is a graph that represents the height of a baseball, , in feet as a function of time, , in seconds after it was hit by Player A. The function  defined by  also represents the height in feet of a baseball  seconds after it was hit by Player B. Without graphing function , answer the following questions and explain or show how you know. Which player’s baseball stayed in flight longer?

Which player’s baseball reached a greater maximum height?

How can you find the height at which each baseball was hit?