To interpret the vertex of the function \( h = 6t^2 - 24t + 30 \), we can use the formula for the vertex of a quadratic function in the form \( h(t) = at^2 + bt + c \). The t-coordinate of the vertex can be found using the formula \( t = -\frac{b}{2a} \).
In this case:
- \( a = 6 \)
- \( b = -24 \)
Calculating the vertex's t-coordinate:
\[ t = -\frac{-24}{2 \cdot 6} = \frac{24}{12} = 2 \]
Next, we substitute \( t = 2 \) back into the function to find the h-coordinate (height):
\[ h(2) = 6(2)^2 - 24(2) + 30 \] \[ = 6(4) - 48 + 30 \] \[ = 24 - 48 + 30 \] \[ = 6 \]
Thus, the vertex of the function is \( (2, 6) \).
This means that the interpretation of the vertex \( (2, 6) \) is as follows:
At \( t = 2 \) seconds, the height \( h \) of the owl is 6 feet. Since this is a quadratic function opening upward, the vertex represents the minimum point, meaning that after 2 seconds, the owl starts to rise from a height of 6 feet.
So, the best interpretation of the vertex is:
(2, 6).