Chapter 7.7, Problem 2ST

To determine

Tofind: theall intercepts of the parabola.

Answer to Problem 2ST

The intercepts of the parabola are $x=2,6\text{ and }y=-6$ .

Explanation of Solution

Given information:

The parabola is $y-2=-\frac{1}{2}{\left(x-4\right)}^2$ .

Calculation: to find the $y$ -intercepts, substitute $x=0$ ,

$\begin{array}{l}y-2=-\frac{1}{2}{\left(x-4\right)}^2\\ y-2=-\frac{1}{2}{\left(0-4\right)}^2\text{ [substitute]}\\ y-2=-8\text{ [square and divide]}\\ y=-6\text{ [simplify]}\end{array}$

to find the $x$ -intercepts, substitute $y=0$ ,

$\begin{array}{l}y-2=-\frac{1}{2}{\left(x-4\right)}^2\\ 0-2=-\frac{1}{2}{\left(x-4\right)}^2\text{ [substitute]}\\ {\left(x-4\right)}^2=4\text{ [cross multiplication]}\\ x-4=\pm 2\text{ [square root]}\\ x=6,2\end{array}$

Thus, The intercepts of the parabola are $x=2,6\text{ and }y=-6$ .