Answer:
C
Step-by-step explanation:
Firstly, we know that the function must be negative due to its shape. This means that the answer cannot be B
Next we can use the equation [tex]x=\frac{-b}{2a}[/tex] that is used in order to find the vertex of the parabola.
A)
[tex]f(x)=-x^2+6x+7\\a=-1,b=6,c=7\\\\x=\frac{-6}{-2} \\x=3[/tex]
As the vertex is at x=3 on the graph, this one could be a contender.
C)
[tex]f(x)=-x^2+6x-7\\a=-1,b=6, c=-7\\\\x=\frac{-6}{-2} \\\\x=3[/tex]
This also could be the equation
D)
[tex]f(x)=-x^2-6x-7\\\\a=-1, b=-6, c=-7\\\\x=\frac{6}{-2} \\\\x=-3[/tex]
This rules option D out.
For this last step, we can look at where the zeroes would be for each equation. (These values are irrational, so we cannot look at specific number)
A)
[tex]f(x)=-(x^2-6x-7)[/tex]
As this equation has a negative value for c, this means that one zero must be positive and the other must be negative.
This means that option A can be ruled out
C)
[tex]f(x)=-(x^2-6x+7)[/tex]
As this equation has a positive value for c, this means that both of the zeroes must be positive. This means that it is the only one that fits all of the criteria.
