Chapter 8.2, Problem 37E

To determine

To describe: two methods to find the zeros of the function $f\left(t\right)=-16t^2+400$ .

Answer to Problem 37E

First method: Set $f\left(t\right)=0$ and solve $-16t^2+400=0$ for t .

Second method: graph the function and find x -intercept.

Explanation of Solution

First set $f\left(t\right)=0$ in the function $f\left(t\right)=-16t^2+400$ and solve for t .

  $\begin{array}{c}-16t^2+400=0\\ 16t^2=400\\ t^2=\frac{400}{16}\end{array}$

  $\begin{array}{c}{t}^2=25\\ t=\pm \sqrt{25}\\ t=\pm 5\end{array}$

Second method is to graph the function $f\left(t\right)=-16t^2+400$ and find the x -intercept.

  

It can be observed that the x -intercept are at $\left(-5,0\right)$ and $\left(5,0\right)$ .

Thus both the methods give the same solution $x=\pm 5$