Chapter 1.4, Problem 6AYU

6. Graph $y=-x^2+15$ using a graphing utility. Create a table of values to determine a good initial viewing window. Use a graphing utility to approximate the intercepts.

To determine

To find:

a. A graph of $y=-x²+15$, using a graphing utility

b. A table of values to determine a good initial viewing window

c. Approximate the intercepts

Answer to Problem 6AYU

Solution:

$x\text{-intercepts are }\left(-\text{3}\text{.873, 0}\right)\text{ and }\left(\text{3}\text{.873, 0}\right)\text{ and }y\text{-intercept is }\left(\text{0, 15}\right)$

Explanation of Solution

Given:

The equation $y=-x²+15$

$x=-2$	$y=-\left(-2\right)²+15$ $=-4+15$ $=11$	$\left(-2,11\right)$
$x=-1$	$y=-\left(-1\right)²+15$ $=-1+15$ $=14$	$\left(-1,14\right)$
$x=0$	$y=-\left(0\right)²+15$ $=15$	$\left(0,15\right)$
$x=\text{ 1}$	$y=-\left(1\right)²+15$ $=-1+15$ $=14$	$\left(1,14\right)$
$x=\text{ 2}$	$y=-\left(2\right)²+15$ $=-4+15$ $=11$	$\left(2,11\right)$

$x\text{-intercepts}$ are $\left(-3.873,0\right)$ and $\left(3.873,0\right)$ and $y\text{-intercept}$ is $\left(0,15\right)$.