"Why = a(x  h)² + k?"  EVERYTHING YOU EVER WANTED TO KNOW ABOUT A QUADRATIC ...
The Quadratic As A Model For Projections 
The Constant in the Equations
Look at the constant terms.

The Linear Coefficient in the Equations
Look at the coefficient of the linear term.

The Quadratic Coefficient in the Equations
Look at the coefficient of the quadratic term. The power on the variable causes the trajectory, path, of the thing to be a parabola, a quadratic function. It makes the path a Ushaped curve. In every equation, the coefficient of the quadratic term is negative. Gravity is bringing the object to the ground even if it is shot upward. The Ushaped curve opens down. If there existed a case in which the more massive object were up, instead of down as on earth, the gravity would be positive and things would not fall but rise and the coefficient of the quadratic term would be positive.

Ex. 3 and Maximum Height

Ex. 4 and What The Equation Doesn't Say

www.mathnstuff.com/math/spoken/here/2class/320/qmotion.htm 