a Find the vertex b Determine maximum or minimum and its val

a) Find the vertex.

b) Determine maximum or minimum and its value.

c) Find the range.

d) Is the function increasing or decreasing?

Thanks in advance

f(x) = -x^2 + 14x -47

Standard quadratice function : y = ax^2 +bx +c

Vertex : at x = -b/2a So, x= -(14)/(-2) = 7

f(7) = -7^2 +14*7 -47 = 2

a) Vertex: ( 7, 2)

b) Since a <0, Its an inverted parabola.

So, it has maximum value.Maximum value = y coordintae of vertex = 2

c)Range : Inverted parabola with vertex ( 7, 2)

So, range (-inf , 2 ]

d) Before the vertex point function is increasing and after the vertex function is decreasing