An owl swoops down from its perch in a tree at 20 feet to catch field mice below. It follows the function h=−6t2−24t+20 . Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
Responses
(1,0)
left parenthesis 1 comma 0 right parenthesis
(−2,44)
left parenthesis negative 2 comma 44 right parenthesis
(44,−2)
left parenthesis 44 comma negative 2 right parenthesis
(−5,0)
To find the vertex of the quadratic function represented by the equation h = -6t^2 - 24t + 20, we can use the formula -b/2a.
In this case, a = -6 and b = -24.
So, the x-coordinate of the vertex is -(-24) / (2 * -6) = 24/ (-12) = -2.
Now, substitute this x-coordinate into the equation to find the y-coordinate of the vertex:
h = -6(-2)^2 - 24(-2) + 20
h = -6(4) + 48 + 20
h = -24 + 48 + 20
h = 44
Therefore, the vertex of the function is (-2, 44).
So, the correct answer is (−2,44)