To find the vertex of the quadratic function given by the equation \( h = -6t^2 - 24t + 20 \), we can use the vertex formula. For a quadratic in the standard form \( ax^2 + bx + c \), the \( t \)-coordinate of the vertex is given by:
\[ t = -\frac{b}{2a} \]
In our equation:
- \( a = -6 \)
- \( b = -24 \)
- \( c = 20 \)
Now, substituting \( a \) and \( b \) into the vertex formula:
\[ t = -\frac{-24}{2 \times -6} = \frac{24}{-12} = -2 \]
Now, we will find the corresponding \( h \)-coordinate by substituting \( t = -2 \) back into the equation.
\[ h = -6(-2)^2 - 24(-2) + 20 \] \[ h = -6(4) + 48 + 20 \] \[ h = -24 + 48 + 20 = 44 \]
Thus, the vertex of the parabola is at \((-2, 44)\).
Therefore, the ordered pair that represents the vertex is:
C. (-2, 44).