Elastic collision of two balls: why kinetic energy formula has 1/2 and squares?

[gcombina]

One ball has a mass of m1 = 0.250 kg and an initial velocity of 5.00 m/s. The other has a mass of m2=0.800 kg and is initially at rest. No external forces act on the balls. What are the velocities of the balls after the collision? Elastic Collision.
On the book I have this formula.

STEP 1#

1/2 m1vf1^2 + 1/2 m2Vf2^2 = 1/2 m1V01^2 + 0

(I am confused for the 1/2 at the beginning and why is squares?)

WHAT?

 

[bobie]

1/2 m1vf1^2 + 1/2 m2Vf2^2 = 1/2 m1V01^2 + 0
(I am confused for the 1/2 at the beginning and why is squares?)

That is the formula of KE and states that the sum of the energy of the balls will be equal to 1/2 0.250*5^2 = 3.125J