Question

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
h
=
6
t
2

−
24
t
+
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

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

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

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

(30,0)

Answer 1

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

In this case:
- \( a = 6 \)
- \( b = -24 \)

Now, substitute in the values:

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

Next, we need to find the height \( h \) at \( t = 2 \):

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

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

Thus, the best interpretation of the vertex in the given options is:

**(2, 6)**.