Q. 92 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 89–96, 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.

$y=-3x^2+19$

Step-by-Step Solution

Answer

The $x$ intercepts are $\left(-2.52,0\right)$ and $\left(2.52,0\right)$.

The $y$ intercept is $\left(0,19\right)$

Step 1. Given Information

The function is $y=-3x^2+19$

Step 2. Create the table for values of x , y

Step 3. Plot these points and connect them

Step 4. Finding x intercept

Put $y=0$

$$\begin{gathered} -3x^2+19=0 \\ -3x^2=-19 \\ {x}^2=6.3 \\ x=-2.52 or 2.52 \end{gathered}$$

Step 5. Finding y intercept

Put $x=0$

$$\begin{gathered} y=-3x^2+19 \\ y=19 \end{gathered}$$