Question

An owl swoops down from its perch in a tree at 30 feet to catch field mice. It follows the function h=6t^2 −24t+30 , where t is the time in seconds and h is the height in feet. Which of the following best interprets the vertex?(1 point)
Responses

(0,30)

(2,6)


(6,2)


(30,0)

Answer 1

The vertex of a quadratic function in the form h = at^2 + bt + c is given by (-b/2a, f(-b/2a)), where f(x) represents the function. In this case, the quadratic function is h = 6t^2 - 24t + 30.

To find the vertex, we can first determine the values of a, b, and c. In this case, a = 6, b = -24, and c = 30.

Using the formula for the x-coordinate of the vertex, we have:
x = -b/2a
x = -(-24) / (2*6)
x = 24 / 12
x = 2

To find the y-coordinate of the vertex, we substitute the value of x into the function:
h = 6(2)^2 - 24(2) + 30
h = 6(4) - 48 + 30
h = 24 - 48 + 30
h = 54 - 48
h = 6

Therefore, the vertex is (2, 6).

The correct answer is: (2, 6)