To find the vertex of the quadratic function \( h = 6t^2 - 24t + 30 \), we can use the formula for the vertex of a parabola given by \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are coefficients from the standard form \( h = at^2 + bt + c \).
In this case, \( a = 6 \) and \( b = -24 \).
Calculating the time \( t \) at which the vertex occurs:
\[ t = -\frac{-24}{2 \cdot 6} = \frac{24}{12} = 2 \]
Next, we will substitute \( t = 2 \) back into the function to find the height \( h \):
\[ h = 6(2^2) - 24(2) + 30 \] \[ h = 6(4) - 48 + 30 \] \[ h = 24 - 48 + 30 \] \[ h = 6 \]
Thus, the vertex of the function is \( (2, 6) \).
The vertex \( (2, 6) \) can be interpreted as follows:
- The owl reaches its maximum height of 6 feet at 2 seconds after it swoops down.
From the options provided, the best interpretation of the vertex is: (2, 6).