Answer:
(3,9)
Step-by-step explanation:
This is a quadratic equation.
A quadratic in standard form is [tex]y=ax^2+bx+c[/tex].
If we compare [tex]y=ax^2+bx+c[/tex] to [tex]y=6x-x^2[/tex], we see there [tex]c=0,b=6,a=-1[/tex].
Now to find the vertex, we first find the x-coordinate of the vertex which is:
[tex]\frac{-b}{2a}[/tex].
So now plug in our values:
[tex]\frac{-6}{2(-1)}=\frac{-6}{-2}=3[/tex]
So the corresponding y-coordinate can be found by the equation that relates x to y: [tex]y=6x-x^2[/tex].
So we are plugging in 3 where we see x: [tex]y=6(3)-3^2=18-9=9[/tex].
So the vertex is (3,9).
