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

Answer 1

To find the vertex of the quadratic function \( h = -6t^2 - 24t + 20 \), we can use the vertex formula for a parabola in the form \( h(t) = at^2 + bt + c \), where the vertex \( t \)-coordinate is given by \( t = -\frac{b}{2a} \).

In your function, \( a = -6 \) and \( b = -24 \).

1. **Find the \( t \)-coordinate of the vertex**:
\[
t = -\frac{-24}{2 \cdot -6} = \frac{24}{-12} = -2
\]

2. **Find the \( h \)-coordinate by substituting \( t = -2 \) back into the function**:
\[
h(-2) = -6(-2)^2 - 24(-2) + 20
\]
\[
= -6(4) + 48 + 20
\]
\[
= -24 + 48 + 20
\]
\[
= 24
\]

Thus, the vertex of the parabola, represented by the ordered pair, is \((-2, 24)\).

So, the correct response from the options provided is:
\((-2, 44)\). (Note there was a computation error in the original calculation above; it should be corrected to \((-2, 24)\) if 24 is not listed among the choices.)

In summary, the vertex is at \((-2, 24)\). If there is a choice \( (-2, 44) \), then it's incorrect; the actual vertex is \( (-2, 24) \).