Chapter 2, Problem 1CA

To determine

To find: The correct inequality symbol to indicate whose throw travels higher.

Answer to Problem 1CA

The height of your throw $<$ The height of your friend’s throw

Explanation of Solution

Given Information: The parabola shows the path of your friend’s throw and path of your throw is modelled by $h\left(x\right)=-16x^2+65x+5$ .

Calculation:

The vertex of your friend’s throw can be calculated as,

The x- intercepts shown in the graph are 0 and 5.

As the axis of symmetry is halfway between $\left(0,0\right)$ and $\left(5,0\right)$

  $\begin{array}{c}a=\frac{0+5}{2}\\ =\frac{5}{2}\\ =2.5\mathrm{......}\text{ (1)}\end{array}$

Here,

• a is the axis of symmetry

so, the vertex is $\left(2.5,80\right)$ and the maximum height is 80 feet.

That is, the height of your friend’s throw is 80.

The vertex of your throw can be calculated as,

For any parabola which is of the form $a{x}^2+bx+c$ , x -coordinate is given by,

  $\begin{array}{c}x=-\frac{b}{a}\\ =-\frac{65}{\left(-16\right)}\\ =\frac{65}{16}\\ =2.03\end{array}$

y- coordinate is given by,

  $\begin{array}{c}y=-16\times {\left(2.03\right)}^2+65\left(2.03\right)+5\\ =71.016\end{array}$

That is, the vertex of your throw is $\left(2.03,71.02\right)$ .

Therefore, the height of your throw is 71.02