Question

Graph each equation. Use the TRACE feature to find the vertex on the graph. Round to the nearest thousandth if necessary.

$y=-5x^2-3x-8$

Short answer

The vertex on the graph is $\left(-0.319,-7.552\right)$.

Step-by-step solution

Step 1. Insert the provided into the calculator.

Take the help of a graphing calculator and press$\boxed{\text{Y=}}$after it insert the provided equation as $Y_1=-5x^2-3x-8$.

Step 2. Determine the graph of the provided equation.

Set the window of the calculator as,

$$\begin{gathered} \text{X}\min =-5 \\ \text{X}\max =5 \\ \text{Xscl}=1 \\ Y\min =-20 \\ Y\max =0 \\ \text{Yscl}=2 \\ \text{Xres}=1 \end{gathered}$$

After the setting of window, press GRAPH button to obtain the graph.

Step 3. Determine the required vertex.

Press TRACE button and use the arrow keys to determine the vertex.

The obtained graph represents the vertex as$\left(-0.3191489,-7.551833\right)$ which means that$\left(-0.3191489,-7.551833\right)$ is the required vertex.

The vertex of the graph after rounding to the nearest thousand is $\left(-0.319,-7.552\right)$.