An owl swoops down from its perch in a tree at 30 feet to catch field mice. It follows the function h=6t2 −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)

Question

Responses

(0,30)
left parenthesis 0 comma 30 right parenthesis

(2,6)
left parenthesis 2 comma 6 right parenthesis

(6,2)
left parenthesis 6 comma 2 right parenthesis

(30,0)

Answer 1

The vertex of the function is given by the formula h = 6t^2 - 24t + 30, where t is the time in seconds and h is the height in feet.

To find the vertex, we need to find the values of t and h that minimize the height of the owl above the ground. This occurs at the vertex of the parabola.

The formula for the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic equation in standard form (h = at^2 + bt + c).

In this case, a = 6 and b = -24. Plugging these values into the formula, we get:

t = -(-24) / 2(6)
t = 24 / 12
t = 2

To find the y-coordinate of the vertex, we substitute the value of t into the equation:

h = 6(2)^2 - 24(2) + 30
h = 6(4) - 48 + 30
h = 24 - 48 + 30
h = 6

Therefore, the vertex of the function is (2, 6).

The correct interpretation of the vertex is (2, 6).