Spring compression -- Ball colliding with a spring-mounted platform

[dge]

Homework Statement

What is the lowest position attained by the platform after it collides elastically with a ball.

Relevant Equations

1/2mv^2=KE
1/2kx^2=Us
mgx=Ug

I've tried establishing a systems of equations with -(1/2)kx^2+mpgx+(1/2)mpvp^2=0, but this leads to an annoying quadratic that when solved does not give one of the listed answers. My thought was that the spring's potential energy is going to be equal to the gravitational potential energy and kinetic energy.

 

[BvU]

I've tried establishing a systems of equations

Don't let us guess. Show your work !
Also: what does it mean that the ball collides elastically with the platform ?

$\$

 

[haruspex]

-(1/2)kx^2+mpgx+(1/2)mpvp^2=0

How did you get the value of $v_p$?