To interpret the vertex of the function \( h = 6t^2 - 24t + 30 \), we first need to find the vertex of the quadratic equation.
The vertex of a quadratic function in the form \( ax^2 + bx + c \) can be found using the formula \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are the coefficients from the equation.
In this case:
- \( a = 6 \)
- \( b = -24 \)
Calculating \( t \):
\[ t = -\frac{-24}{2 \cdot 6} = \frac{24}{12} = 2 \]
Next, we plug \( t = 2 \) back into the height function to find the corresponding height \( h \):
\[ h = 6(2)^2 - 24(2) + 30 \] \[ h = 6(4) - 48 + 30 \] \[ h = 24 - 48 + 30 \] \[ h = 6 \]
So the vertex of the function is at the point \( (2, 6) \).
The vertex represents the maximum height that the owl reaches after 2 seconds.
Thus, the best interpretation of the vertex is:
(2, 6).