Question

On a piece of paper, graph y=-x^2+6x-8 and identify the zeros. Then determine which answer choice matches the graph that you drew and correctly identifies the zeros.

Answer 1

D.

Step-by-step explanation:

To graph the function, we need to identify some points in the graph. Then

`\begin{gathered} \text{ If x = 0} \\ y=-x^2+6x-8 \\ y=-0^2+6(0)-8=-8 \\ \\ \text{ If x = 1} \\ y=-1^2+6(1)-8=-1+6-8=-3 \\ \\ \text{ If x =2} \\ y=-2^2+6(2)-8=-4+12-8=0 \\ \\ \text{ If x = 3} \\ y=-3^2+6(3)-8=-9+18-8=1 \\ \\ \text{ If x = 4} \\ y=-4^2+6(4)-8=-16+24-8=0 \end{gathered}`

Therefore, we will use the points (0, -8), (1, -3), (2, 0), (3, 1), and (4, 0) to graph the function. So, the graph is

Therefore, the zeros are 2 and 4 because (2, 0) and (4, 0) are the points where the graph crosses the x-axis. Thus, the answer is D.