To find the vertex of the quadratic function given by \( h(t) = -6t^2 - 24t + 20 \), we can use the formula for the vertex of a quadratic equation in standard form \( h(t) = at^2 + bt + c \), where \( a = -6 \), \( b = -24 \), and \( c = 20 \).
The \( t \)-coordinate of the vertex can be calculated using the formula:
\[ t = -\frac{b}{2a} \]
Plugging in the values of \( a \) and \( b \):
\[ t = -\frac{-24}{2 \cdot -6} = \frac{24}{-12} = -2 \]
Now, to find the \( h \)-coordinate (or height) at this time, we substitute \( t = -2 \) back into the original equation:
\[ h(-2) = -6(-2)^2 - 24(-2) + 20 \] \[ = -6(4) + 48 + 20 \] \[ = -24 + 48 + 20 \] \[ = 44 \]
Thus, the vertex of the function is at the point \( (-2, 44) \).
Therefore, the ordered pair that represents the vertex is:
(−2, 44)