Question

Graph the function. Be sure to identify Katie's start and end points on the graph.

Answer 1

INFORMATION:

We know that the function that describes Katie's parabolic trajectory is

$h(t)=-16t^2+16t+672$

And we must graph it, identifying Katie's start and end points

STEP BY STEP EXPLANATION:

Since we have a parabola, we can calculate the vertex to graph it

The formula for the vertex is

$x=\frac{-b}{2a}$

In this case, a = -16 and b = 16

Now, replacing in the formula

$x=\frac{-16}{2(-16)}=\frac{1}{2}$

Now, we must replace t = 1/2, to find the coordinate of the vertex

$\begin{gathered} h(\frac{1}{2})=-16(\frac{1}{2})^2+16\cdot\frac{1}{2}+672 \\ h(\frac{1}{2})=676 \end{gathered}$

Then, the coordinate of the vertex is (1/2, 676)

Now, we can find the x intercepts if we equal the function to 0 and solve for t

$\begin{gathered} -16t^2+16t+672=0 \\ -16(t^2-t-42)=0 \\ -16(t-7)(t+6)=0 \\ \text{ Solving for t,} \\ t=7,t=-6 \end{gathered}$

Now, knowing the vertex and the x-intercepts we can graph the function

In the graph we take the positive part of the parabola because t (x-axis) represents time and the time must be positive

The end point would be when h(t) = 0

ANSWER: