Q. 95 - 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.

$5x^2+3y=37$

Step-by-Step Solution

Answer

The $x$ intercepts are $\left(-2.72,0\right) and \left(2.72,0\right)$.

The $y$ intercept is $\left(0,12.34\right)$

Step 1. Given Information

The quadratic equation is $5x^2+3y=37$

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

Step 3. Plot these points and connect them

Step 4. Finding x intercept

Put $y=0$

$$\begin{gathered} 5x^2+3y=37 \\ 5x^2=37 \\ {x}^2=7.4 \\ x=-2.72 or 2.72 \end{gathered}$$

Step 5. Finding y intercept

$$\begin{gathered} Put x=0 \\ 5x^2+3y=37 \\ 3y=37 \\ y=12.34 \end{gathered}$$