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
(1,0)
left parenthesis 1 comma 0 right parenthesis
(44,−2)
left parenthesis 44 comma negative 2 right parenthesis
(−2,44)
left parenthesis negative 2 comma 44 right parenthesis
(−5,0)
left parenthesis negative 5 comma 0 right parenthesis
The equation provided is a quadratic equation in the form of h = -6t^2 - 24t + 20, where h represents the height of the owl above the ground in feet, and t represents time in seconds.
To find the vertex of a quadratic equation in the form of h = at^2 + bt + c, we use the formula for the x-coordinate of the vertex (which, in this context, corresponds to the time t):
t = -b/(2a).
Here, a = -6 and b = -24. Let's calculate the t-coordinate of the vertex:
t = -(-24) / (2 * -6)
= 24 / -12
= -2
Now, to find the corresponding height (h-coordinate) when t = -2, substitute -2 back into the original equation:
h = -6(-2)^2 - 24(-2) + 20
= -6(4) + 48 + 20
= -24 + 48 + 20
= 24 + 20
= 44
So, the vertex of the parabola represented by the equation h = -6t^2 - 24t + 20 is at the point (-2, 44). The correct ordered pair that represents the vertex is:
(-2,44) or in the way it was presented in your question: left parenthesis negative 2 comma 44 right parenthesis.