The height of a football after it’s been kicked can be modeled by the equation
𝒉(𝒕) = −𝟏𝟔𝒕𝟐 + 𝟒𝟓𝒕 + 𝟐. 𝟖 where h(t) represents the height of the ball in feet
and t represents the time in seconds after the ball was kicked.
1. Graph the equation on graph paper. Be sure to label the vertex and the axes.
2. What is a reasonable domain and range for this problem? Explain.
3. What is the maximum height of the ball?
4. Find the height of the ball after it has traveled 2 seconds (show work). Label this point on your graph.
5. Find the height of the ball after it has traveled 1.5 seconds (show work). Label this point on your graph.
6. Explain the meaning of the x-intercepts of your graph in the context of this problem.
7. If the ball is not caught, how long will it take to hit the ground? (Show your work!)