Question

Graph the function $y=-x^2+6x-5$ by making table of values.

Short answer

The graph of the function $y=-x^2+6x-5$ is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=-x^2+6x-5$.

Step 2. Construct the table of values.

Construct the table of values for different $x\text{and}y$ for the function $y=-x^2+6x-5$.

x	y
3	4
1	0
5	0
0	-5
6	-5

Step 3. Sketch the graph of the function.

The graph of the function $y=-x^2+6x-5$ 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.