Notice that the rule of correspondence of g is a quadratic expression:
[tex]g(x)=-x^2+9x-20[/tex]
Since the coefficient of x² is -1, then the parabola must open down.
The options that display a parabola that opens down are A and B.
Observe that option A displays the graph of a parabola whose x-intercepts are 4 and 5, while the option B displays the graph of a parabola whose only x-intercept is 3.
Evaluate g at 3, 4 and 5 to check which numbers make g(x)=0.
[tex]\begin{gathered} g(3)=-(3)^2+9(3)-20=-2 \\ g(4)=-(4)^2+9(4)-20=0 \\ g(5)=-(5)^2+9(5)-20=0 \end{gathered}[/tex]
As we can see, g(x)=0 when x=4 and when x=5.
The only graph that correctly displays this feature is that shown in option A.
Therefore, the graph of g is shown in option A.
The correct choice is option A.
