Question

How do you find the vertex of this equation: y = 6x-x2​

Answer 1

(3,9)

Explanation:

This is a quadratic equation.

A quadratic in standard form is
`y=ax^2+bx+c`.

If we compare
`y=ax^2+bx+c` to
`y=6x-x^2`, we see there
`c=0,b=6,a=-1`.

Now to find the vertex, we first find the x-coordinate of the vertex which is:

`(-b)/(2a)`.

So now plug in our values:

`(-6)/(2(-1))=(-6)/(-2)=3`

So the corresponding y-coordinate can be found by the equation that relates x to y:
`y=6x-x^2`.

So we are plugging in 3 where we see x:
`y=6(3)-3^2=18-9=9`.

So the vertex is (3,9).