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?

A: ( 1,0)

B: ( -5, 0)

C: ( -2, 44)

D: ( 44,-2)

Answers

There are no human answers yet.
Answered by GPT-4o mini
To find the vertex of the quadratic function \( h = -6t^2 - 24t + 20 \), we can use the vertex formula for a quadratic equation \( at^2 + bt + c \). The \( t \)-coordinate of the vertex can be found using the formula \( t = -\frac{b}{2a} \).

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

Substituting the values into the formula:

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

Next, we will find the corresponding \( h \)-coordinate by substituting \( t = -2 \) back into the equation:

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

Calculating this step by step:

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

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

Now we can match this with the options given:

- A: (1, 0)
- B: (-5, 0)
- C: (-2, 44)
- D: (44, -2)

The correct ordered pair that represents the vertex is:

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

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