Chapter 8, Problem 13CR

To determine

To find: It is being asked to find when does the Pumpkin reaches the maximum height and the maximum height.

Answer to Problem 13CR

The Pumpkin reaches its maximum height when t = 2.75 seconds and the maximum height is 133 feet.

Explanation of Solution

Given information: The quadratic function $f(t)=-16t^2+88t+12$

Formula used: The time when it reaches maximum height is $h=\frac{-b}{2a}$ and the maximum height is $f\left(\frac{-b}{2a}\right)$ . Where ‘ a’ is coefficient of $t^2$ term and ‘ b’ is coefficient of t term.

Calculation:

Simply our problem asks for Vertex.

Let’s find the x coordinate of vertex using the formula

From given equation

  $\begin{array}{l}a=-16\\ b=88\end{array}$

Plug in these values into the formula,

X coordinate of vertex $h=\frac{-88}{2(-16)}=\frac{-88}{-32}=2.75$

Let’s find corresponding y coordinate of the vertex.

  $f(2.75)=-16{(2.75)}^2+88(2.75)+12$

  $=-121+242+12$

  $=133$ .

The Pumpkin reaches its maximum height when t = 2.75 seconds and the maximum height is 133 feet.