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
. Plot points to graph the equation. Which ordered pair represents the vertex?

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

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

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

(−2,44)

Answer 1

incorrect it wouldnt be listed unless one was correct try again

Answer 2

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

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

Here, \( a = -6 \) and \( b = -24 \).

Calculating the t-coordinate:

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

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

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

So the vertex of the parabola is at \( (-2, 24) \).

Now, let's assess the given ordered pairs:

1. \( (44, -2) \)
2. \( (-5, 0) \)
3. \( (1, 0) \)
4. \( (-2, 44) \)

None of the provided options contain \( (-2, 24) \), which is the correct vertex. However, if the options involve a misunderstanding or typos, it may be important to verify them against the correct calculation.

### Summary
The vertex of the function \( h(t) = -6t^2 - 24t + 20 \) is at \( (-2, 24) \). None of the listed ordered pairs are correct regarding the vertex based on the calculations.

Answer 3

Apologies for the oversight. Let's accurately determine the vertex of the given function again and match it with the provided options.

The function given is:

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

### Step 1: Calculate the vertex

The t-coordinate of the vertex can be found using the formula:

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

where \( a = -6 \) and \( b = -24 \).

Calculating \( t \):

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

### Step 2: Find the corresponding \( h \) value

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

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

### Resulting vertex

Thus, the vertex is \( (-2, 24) \).

### Comparing with the given options:

1. \( (44, -2) \)
2. \( (-5, 0) \)
3. \( (1, 0) \)
4. \( (-2, 44) \)

None of these ordered pairs show \( (-2, 24) \).

However, the closest point to our calculation is **not present in the options**.

### Checking each option:
- **(44, -2)**: Not correct.
- **(-5, 0)**: Not correct.
- **(1, 0)**: Not correct.
- **(-2, 44)**: Not correct.

I made an error in my prior interpretation.

The **vertex** is \( (-2, 24) \), which is not matched with any of your choices, but if we consider the formulation of the vertex, let’s examine a likely miscommunication in expected outcomes.

Since the vertex value of the ordered pairs does **not exactly match**, could there be an approximation or a miscalculation of the value provided in the list?

If any further analysis is needed, please let me know your consideration for more specific requirements or clarifications. It seems the misunderstanding was around correctly identifying the vertex placement, but numerically, it leads back to produce the vertex value stated consistently from the calculations.

If I've misunderstood the instruction or you would like another correctly assessed problem, please share!