Question

What is the vertex form of `y=-x^2+13x+1`?

Answer 1

y - 173/4 = - (x - 6.5)^2

Explanation:

Set the derivative of y equal to zero to get the value for x at the max/min
-2x +13 = 0 => x = 6.5
Thus y = -(6.5)^2 +13 (6.5) +1 = 173/4
So the vertex is at ( 6.5 , 173/4 )
Thus
y - 173/4 = - (x - 6.5)^2

Check that this is a maximum with
the sign of the 2nd derivative
y'' = -2 => a maximum