An object hits a wall and bounces back with half of its original speed. what is the ratio of the initial kinetic energy to the final kinetic energy?

The ratio of the initial kinetic energy to the final kinetic energy is 4:1

Kinetic energy (KE) is given as i.e. it is proportional to i.e. the square of speed. 

We write the initial kinetic energy is KE.1 =(1/2)mu^2 

When speed is halved, speed will be u/2,

then final kinetic energy will be KE.2 = ( 1/2)m[u/2]^2  = (1/8)mu^2 

Now,ON SOLVING  K,E1 /K.E2, WE GET =  4:1