The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)

1 answer

To find the coordinates of the vertex of the graph, we know that the axis of symmetry is x = -5.

To find the y-coordinate of the vertex, we plug -5 into the function:

f(x) = −x^2 − 10x + 16
f(-5) = -(-5)^2 - 10(-5) + 16
f(-5) = -25 + 50 + 16
f(-5) = 41

Therefore, the coordinates of the vertex of the graph are (-5, 41).

So, the correct option is:
(−5, 41)