A toy gun uses a spring of force constant K. Before being triggered in the upward direction, the spring is compressed by a distance of x. If the mass of the shot is m, on being triggered, it will go up to a maximum height of : 

\(\frac{Kx^2}{2mg}\)

According to the law of conservation of energy,

Elastic potential energy stored in the spring = gravitational potential energy acquired by mass due to shot

\(\Rightarrow mgh = \frac{1}{2} Kx^2\)

\(\Rightarrow h = \frac{Kx^2}{2mg}\)