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)
• (1,0)
• (-2,44)
• (-5,0)
• (11,-2)

Answer 1

To find the vertex of the parabola given by the equation \( h = -6t^2 - 24t + 20 \), we can first rewrite the equation in standard quadratic form, where \( h(t) = at^2 + bt + c \).

Here, \( a = -6 \), \( b = -24 \), and \( c = 20 \).

The vertex of a parabola represented by \( at^2 + bt + c \) can be found using the formula:

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

Plugging in the values of \( a \) and \( b \):

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

Next, we can find the height \( h \) at \( t = -2 \):

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

Calculating it step by step:

1. \( (-2)^2 = 4 \)
2. \( -6 \cdot 4 = -24 \)
3. \( -24 \cdot (-2) = 48 \)
4. Now sum these values: \( -24 + 48 + 20 = 44 \)

So, the vertex (in terms of \( t \) and \( h \)) is:

\[
(-2, 44)
\]

Therefore, the ordered pair that represents the vertex is:

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

Thus, from the options given, the correct answer is:

**(-2, 44)**