An owl swoops down from its perch in a tree at 20 feet to catch field mice below. It follows the function h=−6t^2−24t+20 . Plot points to graph the equation. Which ordered pair represents the vertex?(1 point) Responses (−5,0) left parenthesis negative 5 comma 0 right parenthesis (−2,44) left parenthesis negative 2 comma 44 right parenthesis (44,−2) left parenthesis 44 comma negative 2 right parenthesis (1,0)
To find the vertex of the function, we have to find the values of t and h that correspond to the maximum or minimum point of the parabola.
The vertex of a quadratic function in the form h = at^2 + bt + c is (-b/2a, f(-b/2a)), where f(x) is the value of the function at x.
In our given function h = −6t^2 − 24t + 20, a = -6, b = -24, and c = 20.
The x-coordinate of the vertex is given by -b/2a:
t = -(-24)/2(-6) = 2
To find the y-coordinate of the vertex, we substitute t = 2 into the function:
h = -6(2)^2 - 24(2) + 20
h = -24 - 48 + 20
h = -52
So, the vertex of the function is (2, -52).
Therefore, the correct option is (2, -52).