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(−5,0)left parenthesis negative 5 comma 0 right parenthesis(−2,44)left parenthesis negative 2 comma 44 right parenthesis(1,0)left parenthesis 1 comma 0 right parenthesis(44,−2)
To find the vertex of the quadratic function h=−6t^2−24t+20, we can use the formula t = -b/(2a), where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c).
In this case, a = -6 and b = -24, so t = -(-24)/(2(-6)) = 4.
Now, substitute t = 4 into the equation h=−6t^2−24t+20 to find the corresponding height:
h = -6(4)^2 - 24(4) + 20 = -96 - 96 + 20 = -172.
Therefore, the vertex is (4, -172).
None of the given options match the correct vertex.