Question

An owl swoops down from its perch in a tree at 20 feet to catch field mice below. It follows the function h=−6t^2−24t+20. Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
choose out of these:
A: -5,0
B: -2,44
C: 1,0
D: 44, -2

Answer 1

To find the vertex of the quadratic function \( h(t) = -6t^2 - 24t + 20 \), we can use the vertex formula for a quadratic equation of the form \( ax^2 + bx + c \). The t-coordinate of the vertex is given by:

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

In this case, \( a = -6 \) and \( b = -24 \).

First, we calculate \( t \):

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

Now we substitute \( t = -2 \) back into the equation to find the corresponding \( h(t) \):

\[
h(-2) = -6(-2)^2 - 24(-2) + 20
\]
\[
= -6(4) + 48 + 20
\]
\[
= -24 + 48 + 20
\]
\[
= 44
\]

Thus, the vertex of the function is at the point \( (-2, 44) \).

So, the ordered pair that represents the vertex of the function is:

**B: (-2, 44)**.