Question

The function f given by f(t)=5+30t-32t^2 models the height of the ball in feet. 1. How high was the ball when it was hit? Where do you see this in the equation? 2. Suppose a second ball follows the same trajectory but is hit from 7 feet off the ground. Sketch the graph of the height of the second ball on the same axes. 3. Write an equation for a function g that defines the height g(t) , in feet, of the second ball hit from 7 feet off the ground in terms of f(t).

Answer 1

The ball was 5 feet high when it was hit. The graph of the second ball's height can be plotted by modifying the original equation. The equation for the height of the second ball is g(t) = 12 + 30t - 32t^2.

Step-by-step explanation:

The equation given to model the height of the ball is f(t) = 5 + 30t - 32t^2. To find the height of the ball when it was hit, we need to find the value of f(t) at t = 0. Substituting t = 0 into the equation, we get f(0) = 5 + 30(0) - 32(0)^2 = 5 feet. So, the ball was 5 feet high when it was hit.

To sketch the graph of the height of the second ball hit from 7 feet off the ground, we need to modify the equation to account for the initial height. The equation for the second ball, g(t), would be g(t) = 7 + 5 + 30t - 32t^2. We can plot this equation on the same axes as the first ball's graph to compare their heights.

Thus, the equation for the height of the second ball is g(t) = 12 + 30t - 32t^2.