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

Dec 25, 2016

Max. at vertex (3, 13)

#### Explanation:

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