To find the maximum height of the arrow, we can analyze the height function given by the formula:
\[ h(t) = -16t^2 + 128t \]
This is a quadratic function in the standard form \(h(t) = at^2 + bt + c\), where \(a = -16\), \(b = 128\), and \(c = 0\). The maximum value of a quadratic function occurs at the vertex, which can be found using the formula:
\[ t = -\frac{b}{2a} \]
Substituting the values of \(a\) and \(b\):
\[ t = -\frac{128}{2 \times -16} = \frac{128}{32} = 4 \]
Now, we substitute \(t = 4\) back into the height function to find the maximum height:
\[ h(4) = -16(4^2) + 128(4) \] \[ = -16(16) + 128(4) \] \[ = -256 + 512 \] \[ = 256 \]
Thus, the maximum height of the arrow is 256 feet.
The correct answer is C. 256 ft.