Question

An owl swoops down from its perch in a tree at 20 feet to catch field mice below. It follows the function h=−6t2−24t+20
ℎ
=
−
6
𝑡
2
−
24
𝑡
+
20
. Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
Responses

(−2,44)
(
−
2
,
44
)
left parenthesis negative 2 comma 44 right parenthesis

(44,−2)
(
44
,
−
2
)
left parenthesis 44 comma negative 2 right parenthesis

(−5,0)
(
−
5
,
0
)
left parenthesis negative 5 comma 0 right parenthesis

(1,0)

Answer 1

To find the vertex of the quadratic function \( h = -6t^2 - 24t + 20 \), we can use the vertex formula for a parabola, which is given by \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are the coefficients from the standard form \( at^2 + bt + c \).

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

Now, we can find the \( t \)-coordinate of the vertex:

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

Now that we have \( t = -2 \), we can find the corresponding \( h \)-coordinate by plugging \( t \) back into the original function:

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

Calculating step-by-step:

1. \( (-2)^2 = 4 \)
2. \( -6 \cdot 4 = -24 \)
3. \( -24 \cdot -2 = 48 \)
4. Now substitute:
\[
h = -24 + 48 + 20 = 44
\]

So the vertex is at the point \( (-2, 44) \).

The correct ordered pair that represents the vertex is:

\[
\boxed{(-2, 44)}
\]