Question

given the function f(x)=-x^2+8x+9, state whether the vertex the represents a maximum or minimum point for the function

Answer 1

Should be a maximum as the negative in front of the first x signifies a negative (downward facing) parabola 

Answer 2

If you had
ax^2+bx+c
a is the leading term
when a>0, the parabola opens up and therfor has a minimum point and no max since it goes up infinitely

when a<0, the parabola opens down and therefor has a maximum point and not min since it goes down infinitely

-x^2+8x+9
-1<0
opens down
has max
vertex=max