Answer: OPTION C
Step-by-step explanation:
Calculate the x-coordinate of the vertex of the parabola of the function [tex]f(x)[/tex], with the following formula:
[tex]x=-\frac{b}{2a}[/tex]
In this case:
[tex]b=8\\a=-2[/tex]
Substitute values:
[tex]x=-\frac{8}{2(-2)}=2[/tex]
Substitute [tex]x=2[/tex] into the funtion [tex]f(x)[/tex] to find the y-coordinate of the vertex. Then:
[tex]y=-2(2)^2+8(2)-1\\y=7[/tex]
Therefore, the maximum value of [tex]f(x)[/tex] is:
[tex]y=7[/tex]
As you can see, the y-coordinate of the vertex of the parabola [tex]g(x)[/tex] is less than 7, therefore, you can conclude that the function that has the greater maximum value is:
[tex]f(x)[/tex]
