To find the vertex of the quadratic function given by \( h(t) = -6t^2 - 24t + 20 \), we can use the vertex formula:
The x-coordinate of the vertex \( t \) can be found using: \[ t = -\frac{b}{2a} \] In this equation, \( a = -6 \) and \( b = -24 \).
Now, substituting in the values: \[ t = -\frac{-24}{2 \times -6} = \frac{24}{-12} = -2 \]
Next, we will find the h-coordinate (height) of the vertex by substituting \( t = -2 \) back into the function: \[ h(-2) = -6(-2)^2 - 24(-2) + 20 \] Calculating this step-by-step: \[ h(-2) = -6(4) + 48 + 20 \] \[ h(-2) = -24 + 48 + 20 \] \[ h(-2) = 24 \]
Thus, the vertex of the function is \((-2, 24)\).
None of the provided answer choices matches the computed vertex. The correct vertex point is \((-2, 24)\).
It looks like there might have been a small mix-up with the answer choices given. Since \((-2, 24)\) isn't among them, none of the listed options is correct. If you have to select one based on closeness to our computed vertex, unfortunately, we would have no valid options to give a correct answer based on the given values.