Elastic Potential Energy

Stretching or squeezing a spring takes work, and the spring stores it as elastic potential energy: the area under the F-x graph.

The stored energy is the shaded area: half of x times kx.

$$\mathrm{PE}_{\text{spring}} = \tfrac{1}{2} k x^2$$

$x$ is measured from the natural length. Twice the stretch stores four times the energy.