To find the time \( t \) when the water balloon reaches its maximum height, we can use the vertex formula for a quadratic function in the form \( h = at^2 + bt + c \). The time at which the maximum height occurs is given by:
\[ t = -\frac{b}{2a} \]
In your equation \( h = -2t^2 + 8t + 2 \):
- \( a = -2 \)
- \( b = 8 \)
Plugging these values into the vertex formula:
\[ t = -\frac{8}{2 \cdot -2} = -\frac{8}{-4} = 2 \]
So, the water balloon will reach its maximum height at 2 seconds.
Next, we'll find the maximum height by substituting \( t = 2 \) back into the function \( h(t) \):
\[ h(2) = -2(2^2) + 8(2) + 2 \]
Calculating this:
\[ h(2) = -2(4) + 16 + 2 \] \[ = -8 + 16 + 2 \] \[ = 10 \]
Thus, the maximum height of the water balloon will be 10 feet.
Final answers:
- The water balloon will reach its maximum height at 2 seconds.
- The maximum height of the water balloon will be 10 feet.