Question

use your graphing calculator to sketch the graph of the following quadratic function, then determine the domain and range.

g(x) = -x² + 9x - 8

sketch the graph of the function in the viewing window -10,10 × -15,15. choose the correct graph below.

○ a. ○ b. ○ c. ○ d.

Explanation:

Step1: Analyze the quadratic function

The function is \( g(x) = -x^2 + 9x - 8 \). The coefficient of \( x^2 \) is -1, which is negative, so the parabola opens downward.

Step2: Identify the correct graph

Graphs A and B open upward (since they have a minimum point), so they can be eliminated. Now, between C and D, we can find the roots of the function to check. Set \( g(x) = 0 \), so \( -x^2 + 9x - 8 = 0 \) or \( x^2 - 9x + 8 = 0 \). Factoring, we get \( (x - 1)(x - 8) = 0 \), so the roots are \( x = 1 \) and \( x = 8 \). The parabola should cross the x - axis at \( x = 1 \) and \( x = 8 \). Graph C has the parabola crossing the x - axis at appropriate positive x - values (since 1 and 8 are positive) and opening downward. Graph D seems to have the roots in a different position. So the correct graph is C.

Answer:

C