Interpreting Graphs of Quadratic Functions

7.6.4 Interpreting Graphs of Quadratic Functions

7.6.4 • Interpreting Graphs of Quadratic Functions

Cool Down

The height in feet, $h$ , of a stomp rocket (propelled by a short blast of air) above the ground after $t$ seconds is given by the equation $h (t) = 5 + 100 t - 16 t^{2}$ . Here is a graph that represents $h$ .

A parabola on a coordinate grid. The x-axis represents time in seconds and the y-axis represents the height above the ground in feet. The x-axis scale is 1 and extends from 0 to 7. The y-axis scale is 50 extends from 0 to 200.

How does the 5 in the equation relate to the graph?

Compare your answer:

The graph intersects the vertical axis at 5.

What does $100 t$ in the equation mean in terms of the rocket?

Compare your answer:

It indicates that the initial velocity of the rocket was 100 feet per second upward.

What does the $- 16 t^{2}$ mean in terms of the rocket?

Compare your answer:

This indicates the effect of gravity pulling the rocket back toward Earth.

About when does the rocket hit the ground?

Compare your answer:

At about 6.3 seconds.