Question

How do you tell whether the function has a max or min and identify the coordinates of it `f(x)=-x^2+6x+4`?

Answer 1

Max. at vertex (3, 13)

Explanation:

`f(x) = - x^2 + 6x + 4`
Since a = -1 < 0, the parabola graph opens downward. There is a max. at the vertex.
x- coordinate of vertex:
`x = -b/(2a) = (-6)/(-2) = 3`
y-coordinate of vertex:
f(3) = - 9 + 18 + 4 = 13
Max. at Vertex (3, 13)
graph{- x^2+ 6x + 4 [-40, 40, -20, 20]}