Chapter 2.1, Problem 43E

To determine

To find: A function modeling the second jump of the red kangaroo.

Answer to Problem 43E

The function modeling the second jump is $g(x)=-0.03{(x-14)}^2+11$ .

Explanation of Solution

Given information: The function representing the jump of the kangaroo is $h(x)=-0.03{(x-14)}^2+6$ , where $x$ is the horizontal distance travelled and $h(x)$ is the height.

Calculation:

Let us draw a graph representing the given function:

  

From the graph, $h(28.142)=0$ .

So, the kangaroo travels a horizontal distance of $28.142feet$ .

When the kangaroo jumps from a higher location, it lands $5feet$ farther away, i.e., at the point $x=28.142+5=33.142$ .

The function $g$ that models the second jump must be $0$ at $x=33.142$ . So,

  $\begin{array}{l}g(x)=h(x)+5\\ =-0.03{(}^x+6+5\\ =-0.03{(}^x+11\end{array}$

Thus, the function modeling the second jump is $g(x)=-0.03{(x-14)}^2+11$ .