To find the maximum height of the arrow, we can use the given quadratic equation:
\[ h = -16t^2 + 80t + 25 \]
This equation is in the standard form \( h = at^2 + bt + c \), where \( a = -16 \), \( b = 80 \), and \( c = 25 \).
The maximum height of a quadratic function in this form occurs at the vertex, which can be found using the formula:
\[ t = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ t = -\frac{80}{2 \times -16} \] \[ t = -\frac{80}{-32} \] \[ t = 2.5 \text{ seconds} \]
Now, we can substitute \( t = 2.5 \) back into the height equation to find the maximum height \( h \):
\[ h = -16(2.5)^2 + 80(2.5) + 25 \] \[ h = -16(6.25) + 200 + 25 \] \[ h = -100 + 200 + 25 \] \[ h = 125 \]
Thus, the maximum height of the arrow is:
125 feet.