Chapter 2.2, Problem 73E

To determine

To calculate: The mouse can jump over the fence that is 3 feet high.

Answer to Problem 73E

The mouse cannot jump the fence.

Explanation of Solution

Given Information: Jump of a mouse is modeled by the path $y=-0.2x^2+1.3x$ where x is the distance covered by the mouse in feet and y is the corresponding height in feet.

Calculation:

The x -coordinate of the vertex of the parabola of the form $y=a{x}^2+bx+c$ is given by $x=-\frac{b}{2a}$ and y- coordinate is $f\left(x\right)$ .

The x- coordinate of the parabola $y=-0.2x^2+1.3x$ is,

  $\begin{array}{c}x=-\frac{b}{2a}\\ =-\frac{1.3}{2\left(-0.2\right)}\left(b=1.3,a=-0.2\right)\\ =\frac{1.3}{0.4}\\ =3.25\end{array}$

The y -coordinate is,

  $\begin{array}{l}y=-0.2x^2+1.3x\\ =-0.2{\left(3.25\right)}^2+1.3\left(3.25\right)\\ =2.1125\end{array}$

Therefore, the vertex is $\left(3.25,2.1125\right)$ .

Thus, the mouse can jump a maximum height of 2.1125 feet and since the height of the fence is 3 feet, the mouse cannot jump the fence.