An owl swoops down from its perch in a tree at 20 feet to catch field mice below. If follows the function h = -6t^2 - 24t + 20. Plot points to graph the equation. Which ordered pair represents the vertex?
A. (1, 0)
B. (-5, 0)
C. (44, -2)
D. (-2, 44)
To find the vertex of the given function, we need to first rewrite the function in vertex form: h = a(t - h)^2 + k, where (h, k) represents the vertex.
For the given function h = -6t^2 - 24t + 20, we need to manipulate it to the vertex form.
h = -6t^2 - 24t + 20
h = -6(t^2 + 4t) + 20
h = -6(t^2 + 4t + 4 - 4) + 20
h = -6((t + 2)^2 - 4) + 20
h = -6(t + 2)^2 + 24 + 20
h = -6(t + 2)^2 + 44
From the final equation, we can see that the vertex is (-2, 44).
Therefore, the correct answer is D. (-2, 44).