To find the vertex of the quadratic function \( h(t) = -6t^2 - 24t + 20 \), we can use the vertex formula for a quadratic function in the standard form \( ax^2 + bx + c \):
The x-coordinate (or in this case, the t-coordinate) of the vertex is given by the formula:
\[ t = -\frac{b}{2a} \]
where \( a = -6 \) and \( b = -24 \).
Substituting these values into the formula:
\[ t = -\frac{-24}{2 \cdot -6} = \frac{24}{-12} = -2 \]
Now, plug \( t = -2 \) back into the function \( h(t) \) to find the height (h-coordinate) of the vertex:
\[ h(-2) = -6(-2)^2 - 24(-2) + 20 \]
Calculating this:
\[ h(-2) = -6(4) + 48 + 20 \] \[ h(-2) = -24 + 48 + 20 \] \[ h(-2) = 24 \]
Thus, the vertex of the quadratic function is at the point:
\[ (-2, 24) \]
So, the ordered pair that represents the vertex is \((-2, 24)\).