Answer
(a)
vertex: $(-2, 8)$
x-intercepts: $-6$ and $2$
y-intercept: $6$
(b)
maximum value: $8$
(c)
domain: $(-\infty, +\infty)$
range: $-\infty, 8]$
Work Step by Step
RECALL:
(a)
The parabola opens downward so the vertex is the maximum point of the graph.
Thus, the vertex is $(-2, 8)$
The graph clearly shows that the x-intercepts are $-6$ and $2$ while the y-intercept is $6$
(b) The parabola opens downward so the function has a maximum value, which is the y-coordinate of the vertex.
Thus, the maximum value if $f$ is $8$.
(c) The domain of a quadratic function is the set of all real numbers, $(-\infty, +\infty)$
The y-values of the function are from $8$ and below.
Thus, the range is $(-\infty, 8]$.
