Chapter 1.1, Problem 91AYU

In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window.

$y=2x^2-15$

To determine

To sketch: The equation $y = 2x^{\mathrm{2 }}-\mathrm{ 15}$ and approximate the intercepts rounded to two decimal places.

Answer to Problem 91AYU

$x\text{-intercept}\text{ is }\pm 2.74\text{ and }y\text{-intercept}\text{ is }-15$

Explanation of Solution

Given:

The equation $y = 2x^{\mathrm{2 }}-\mathrm{ 15}$.

Interpretation:

$x =-2$	$y = 2{(-2)}^2-15 = 2*4-15 = 8-15 = -7$
$x =-1$	$y = 2{(-1)}^2-15 = 2*1-15 = 2-15 = -13$
$x =1$	$y = 2{(1)}^2-15 = 2*1-15 = 2-15 = -13$
$x =0$	$y = 2{(0)}^2-15 = 2*0-15 = 0-15 = -15$
$x =2$	$y = 2{(2)}^2-15 = 2*4-15 = 8-15 = -7$
$y =0$	$0=2x^2-15,2x^2=15,x^2=\frac{15}{2},x=\pm \sqrt{\frac{15}{2}}=\pm 2.739=\pm 2.74$

$x\text{-intercepts}$ are $\pm 2.74$ and $y\text{-intercept}$ is $-15$