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

Question

, 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

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

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

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

(2,6)

Answer 1

To find the vertex of the quadratic function \( h = 6t^2 - 24t + 30 \), we can use the formula for the vertex of a quadratic equation in the form \( ax^2 + bx + c \). The vertex occurs at \( t = -\frac{b}{2a} \).

Here, \( a = 6 \) and \( b = -24 \).

Calculating the vertex:

\[ t = -\frac{-24}{2 \times 6} = \frac{24}{12} = 2 \]

Now, we can find the corresponding height \( h \) at \( t = 2 \):

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

Thus, the vertex of the function is \( (2, 6) \).

The correct interpretation of the vertex is (2, 6), indicating that at \( t = 2 \) seconds, the height of the owl is 6 feet.