You can take any equation of motion solve for v and then substitute in the equation above. I am working on trying to derive KE or Etrans32nRT. Combining the 2 expressions we get.
Practically speaking you can just memorize that h b 2a and then plug your value for h back in to y to calculate kIf youre allowed to use this formula you can then more quickly find the vertex because simply calculating h b 2a and then finding k is a lot faster than completing the square.
Also surfers like to ride on them. Start from the work-energy theorem then add in Newtons second law of motion. The formula for calculating kinetic energy KE is KE 05 x mv2. Derivation using algebra alone and assuming acceleration is constant.