The function \( h = -6t^2 - 24t + 20 \) is a quadratic function that describes the height of the owl above the ground with respect to time \( t \). To find the vertex of this parabola, we can use the formula for the vertex \( t = -\frac{b}{2a} \).
In the given equation:
- \( a = -6 \)
- \( b = -24 \)
Now, we can substitute the values into the formula for the vertex:
\[ t = -\frac{-24}{2 \cdot -6} = \frac{24}{-12} = -2 \]
Next, we can find the height \( h \) by substituting \( t = -2 \) back into the function:
\[ h = -6(-2)^2 - 24(-2) + 20 \] \[ = -6(4) + 48 + 20 \] \[ = -24 + 48 + 20 \] \[ = 24 + 20 \] \[ = 44 \]
Thus, the vertex of the parabola is at \( (-2, 44) \).
Among the provided options, the correct ordered pair representing the vertex is:
(-2, 44).