Question

find the vertex, the axis of symmetry, and the maximum and minimum value.
f(x) = -1/5 (x-1)^2 +1

Answer 1

The equation: y=-1/5(x-1)^2 + 1
can be written as: -5y - 1 = (x-1)^2
or as
-5(y + (1/5)) = (x-1)^2

This is of the form: 4p(y-k) = (x-h)^2, where (h,k) is the vertex and p is the distance from the vertex to the focus.

Answer 2

So..

4p(y - k) = (x-h)^2
-5(y + (1/5)) = (x-1)^2

It's obvious (1, -1/5) is the vertex. Also, 4p = -5. So p=-5/4. The negative means this parabola is opening downwards. The distance from the vertex to the focus is 5/4.