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) Responses (1,0) left parenthesis 1 comma 0 right parenthesis (−2,44) left parenthesis negative 2 comma 44 right parenthesis (−5,0) left parenthesis negative 5 comma 0 right parenthesis (44,−2)

Answer 1

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

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

In this case, \( a = -6 \) and \( b = -24 \).

Plugging in the values:

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

Now we can find the \( h \) coordinate of the vertex by substituting \( t = -2 \) back into the equation:

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

Calculating step by step:

1. \( (-2)^2 = 4 \)
2. \( -6 \times 4 = -24 \)
3. \( -24 \times -2 = 48 \)
4. Adding: \( -24 + 48 + 20 = 44 \)

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

Thus, the correct ordered pair representing the vertex is:

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