To find the vertex of the quadratic function \( h = 6t^2 - 24t + 30 \), we can use the vertex formula. The vertex of a quadratic function in the form \( h = at^2 + bt + c \) can be found using the formula for the time \( t \) at which the vertex occurs:
\[ t = -\frac{b}{2a} \]
In your function:
- \( a = 6 \)
- \( b = -24 \)
Plugging these values into the vertex formula:
\[ t = -\frac{-24}{2 \cdot 6} = \frac{24}{12} = 2 \]
Now we can find the height \( h \) at this time \( t = 2 \):
\[ h = 6(2)^2 - 24(2) + 30 \] \[ h = 6 \cdot 4 - 48 + 30 \] \[ h = 24 - 48 + 30 \] \[ h = 6 \]
Thus, the vertex of the function is at the point \((2, 6)\), which gives the maximum height reached by the owl.
The correct interpretation of the vertex is:
• (2, 6)