Question 622054
Determine where the function is increasing and where it is decreasing.

f(x)=-x^2-4x+5
.
Because it is a polynomial of degree 2, we know it is a parabola.
And, because the coefficient associated with the x^2 term is negative, we know it opens downwards.  So, the max will be at the vertex.
.
Axis of symmetry:
x = -b/(2a)
x = -(-4)/(2(-1))
x = 4/(-2)
x = -2
.
function is increasing in the range of:
(-oo, -2)
function is decreasing in the range of:
(-2, +oo)
where oo indicates infinity