To interpret the vertex of the quadratic function given by the equation \( h = 6t^2 - 24t + 30 \), we need to find the time \( t \) at which the height \( h \) reaches its maximum or minimum point.
The vertex of a quadratic function in the form \( h = at^2 + bt + c \) can be found using the formula:
\[ t = -\frac{b}{2a} \]
In your equation, \( a = 6 \) and \( b = -24 \). Plugging in the values:
\[ t = -\frac{-24}{2 \cdot 6} = \frac{24}{12} = 2 \]
Now, we need to find \( h \) when \( t = 2 \):
\[ h = 6(2^2) - 24(2) + 30 \] \[ h = 6(4) - 48 + 30 \] \[ h = 24 - 48 + 30 = 6 \]
Thus, the vertex of the function is at the point \( (2, 6) \).
In the context of the problem, this means that at \( t = 2 \) seconds, the owl is at a height of \( 6 \) feet, which represents either a minimum height if the parabola opens upwards (which it does, since \( a = 6 > 0 \)).
Therefore, the best interpretation of the vertex is:
(2, 6).
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