To find the vertex of the quadratic function \( h = 6t^2 - 24t + 30 \), we can use the vertex formula for a quadratic equation in the standard form \( ax^2 + bx + c \), where the vertex \( t \) coordinate can be found using:
\[ t = -\frac{b}{2a} \]
In this case:
- \( a = 6 \)
- \( b = -24 \)
- \( c = 30 \)
Substituting in the values:
\[ t = -\frac{-24}{2 \times 6} = \frac{24}{12} = 2 \]
Now we need to find the corresponding height \( h \) at \( t = 2 \):
\[ h = 6(2)^2 - 24(2) + 30 \] \[ h = 6(4) - 48 + 30 \] \[ h = 24 - 48 + 30 \] \[ h = 6 \]
Thus, the vertex of the function is \( (2, 6) \).
The best interpretation of the vertex, therefore, is \( (2, 6) \), which indicates that at \( t = 2 \) seconds, the height of the owl is \( 6 \) feet.
So the correct response is \((2, 6)\).