Question

he water from a sprinkler follows the path of the equation h(x)=-0.28 (x-3.09)^2 +3.27 What is the maximum height the water will reach in feet?

Answer 1

we have
y=a(x-h)²+k
(h,k) is the vertex
if a<0, then the parabola opens down and the vertex is the maximum

so

h(x)=-0.28(x-3.09)²+3.27
-0.28<0 so the parabola opens down and the vertex is a maximum
the vertex is (3.09,3.27)
in (h,k), h is the independent vairable, like time, and k would be the height
so the maximum height is 3.27ft