Answer
Option (d)
Work Step by Step
RECALL:
(1) The graph of the quadratic function $y=ax^2+bx+c$ is a parabola that opens:
(i) downward when $a \lt 0$; or
(ii) upward when $a \gt 0$
(2) A parabola that open upward has the vertex as its minimum point, while a parabola that opens downward has the vertex as its maximum point.
The given function has its maximum value at its vertex.
This means that the parabola opens downward.
Thus, $a \lt 0$.
The answer is Option (d).
