To find the ordered pair that represents the vertex of the quadratic function \( h(t) = -6t^2 - 24t + 20 \), we can use the vertex formula for a quadratic equation in the standard form \( ax^2 + bx + c \).
The vertex \( t \) coordinate is given by the formula:
\[ t = -\frac{b}{2a} \]
where \( a = -6 \) and \( b = -24 \).
Plugging in the values:
\[ t = -\frac{-24}{2 \cdot -6} = \frac{24}{-12} = -2 \]
Now, we substitute \( t = -2 \) back into the function \( h(t) \) to find the corresponding \( h \) value (the height):
\[ h(-2) = -6(-2)^2 - 24(-2) + 20 \] \[ = -6(4) + 48 + 20 \] \[ = -24 + 48 + 20 \] \[ = 44 \]
Thus, the vertex of the function is at the ordered pair:
\[ \text{Vertex} = (-2, 44) \]
So, the ordered pair representing the vertex is \((-2, 44)\).
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