Question

The curve produced by the water coming from a fountain is sketched on the graph.


Which function does the graph represent?

f(x) = (x – 2)2 + 3
f(x) = –(x – 2)2 + 3
f(x) = (x + 2)2 + 3
f(x) = –(x + 2)2 + 3

Answer 1

f(x) = −(x + 2)^2 + 3

Reason: the parabola opens downward (negative leading coefficient) and its vertex is at (−2, 3), so it has the form f(x)=a(x−h)^2+k with a<0 and (h,k)=(−2,3).