Question

Graph the function $y=\frac{1}{2}{x}^2+2x-6$ by making table of values.

Short answer

The graph of the function $y=\frac{1}{2}{x}^2+2x-6$ is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=\frac{1}{2}{x}^2+2x-6$.

Step 2. Construct the table of values.

Construct the table of values for different $x\text{and}y$ for the function $y=\frac{1}{2}{x}^2+2x-6$.

x	y
-6	0
2	0
-4	-6
0	-6
-2	-8

Step 3. Sketch the graph of the function.

The graph of the function $y=\frac{1}{2}{x}^2+2x-6$ can be constructed by plotting the ordered pair of $\left(x,y\right)$ from the table.

Step 4. Interpretation the graph of the function.

From the graph it can be interpreted that the graph cuts x-axis at two points. Hence it will have two real solutions.