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

Question

. Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
Responses

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

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

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

(−5,0)

Answer 1

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

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

In this equation:

• \( a = -6 \)
• \( b = -24 \)

Now, substituting these values into the vertex formula:

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

Next, to find the corresponding \( h \)-coordinate of the vertex, substitute \( t = -2 \) back into the original function:

\[ h(-2) = -6(-2)^2 - 24(-2) + 20 \] \[ = -6(4) + 48 + 20 \] \[ = -24 + 48 + 20 \] \[ = 44 \]

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

Therefore, the ordered pair that represents the vertex is:

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