Chapter 8.5, Problem 85E

a.

To determine

To find the wideness in the satellite dish.

Answer to Problem 85E

  $4\text{ feet}$

Explanation of Solution

Given:

The given cross-section of dish is $y=\frac{1}{8}(x^2-4)$ where, $x\text{ and }y$ are measured in feet.

Calculation:

From, the graph the width is the distance form $x=-2$ to $x=2$ .

Therefore wideness is $4\text{ feet}$

b.

To determine

To find the depth of the satellite dish.

Answer to Problem 85E

  $\text{0}\text{.5 feet}$

Explanation of Solution

Given:

The given cross-section of dish is $y=\frac{1}{8}(x^2-4)$ where, $x\text{ and }y$ are measured in feet.

Calculation:

From, the graph the depth is from the origin to the vertex $(0,-0.5)$ .

Therefore depth is $\text{0}\text{.5 feet}$

c.

To determine

To find the quadratic equation in standard form that models the cross section of the satellite dish.

Answer to Problem 85E

  $y=\frac{1}{6}(x^2-9)$

Explanation of Solution

Given:

The given cross-section of dish is $y=\frac{1}{8}(x^2-4)$ where, $x\text{ and }y$ are measured in feet.

Calculation:

Using the x-intercept form to find the quadratic equation.

  

  $\begin{array}{l}y=a(x-p)(x-q)\\ y=a(x+3)(x-3)\end{array}$

Use the other point $(0,-1.5)$ to find the value of $a$

  $\begin{array}{l}-1.5=a(x+3)(x-3)\\ a=\frac{1}{6}\end{array}$

Therefore the quadratic equation is-

  $y=\frac{1}{6}(x^2-9)$