Answer
$y = -(x-3)^2 + 4$, or (H)
Work Step by Step
Given an axis of symmetry and a range, we should use vertex form: $y = a(x-h)^2 + k$
We know that the range of the graph is less than or equal to 4. When the range has an upper bound, it means that $a < 0$. Given the choices, a would have to be -1.
h is the axis of symmetry, so we know that is -3.
The upper bound is 4, so we can set k to 4. So, apply this to vertex form:
$y = a(x-h)^2 + k = -(x+3)^2 + 4$
