To find the vertex of the quadratic function given by \( h = -6t^2 + 33t + 6 \), we can use the formula for the x-coordinate of the vertex of a parabola represented by \( ax^2 + bx + c \), which is:
\[ t = -\frac{b}{2a} \]
In this equation:
- \( a = -6 \)
- \( b = 33 \)
Now substitute these values into the formula:
\[ t = -\frac{33}{2(-6)} = \frac{33}{12} = 2.75 \]
Next, we calculate the height \( h \) at \( t = 2.75 \):
\[ h = -6(2.75)^2 + 33(2.75) + 6 \] \[ = -6(7.5625) + 33(2.75) + 6 \] \[ = -45.375 + 90.75 + 6 \] \[ = -45.375 + 96.75 \] \[ = 51.375 \]
Thus, the ordered pair representing the vertex is:
\[ (2.75, 51.375) \]
So the correct response is:
(2.75, 51.375)