Question

An owl swoops down from its perch in a tree al 30 feef 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)

• (2,6)

• (0,2)

• (0,30)

• (30,0)

Answer 1

To find the vertex of the quadratic function \( h = 6t^2 - 24t + 30 \), we can use the vertex formula. The vertex of a quadratic function in the form \( h = at^2 + bt + c \) can be found using the formula for the time \( t \) at which the vertex occurs:

\[
t = -\frac{b}{2a}
\]

In your function:

- \( a = 6 \)
- \( b = -24 \)

Plugging these values into the vertex formula:

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

Now we can find the height \( h \) at this time \( t = 2 \):

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

Thus, the vertex of the function is at the point \((2, 6)\), which gives the maximum height reached by the owl.

The correct interpretation of the vertex is:

• **(2, 6)**