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

Question

ℎ
=
−
6
𝑡
2
−
24
𝑡
+
20
. Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
Responses

(1,0)
(
1
,
0
)
left parenthesis 1 comma 0 right parenthesis

(−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

Answer 1

To find the vertex of the function \( h(t) = -6t^2 - 24t + 20 \), we can use the vertex formula for a quadratic equation given in the form \( at^2 + bt + c \). The vertex \( t \)-coordinate can be found using:

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

In this case, we have:

• \( a = -6 \)
• \( b = -24 \)

Substituting these values into the formula:

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

Now we find the \( h \)-coordinate (the height) by substituting \( t = -2 \) back into the original equation:

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

Thus, the vertex of the function is at the point \((-2, 24)\).

Now looking at the options provided, the correct ordered pair representing the vertex is:

(−2, 24)

So the correct response is:

\[ (-2, 24) \]