"Why = a(x  h)² + k?"  EVERYTHING YOU EVER WANTED TO KNOW ABOUT A QUADRATIC BUT WERE AFRAID TO ASK 
The Quadratic, y = ax^{2} + bx + c

Quadratic  
Quadratic?  Quadratic: x^{2}, or 2x^{2} or 3x^{2} or ax^{2}.  
Quadratic:  NOT constant (2, 3, a).  
Quadratic:  NOT linear (2x or 3x or ax).  
Quadratic:  NOT cubic (2x^{3} or 3x^{3} or ax^{3}).  
Quadratic:  NOT quartic (3x^{4}), or higher.  
Quadratics are polynomials where the highest degree of the variable is 2. Quadratics are polynomials like ax^{2} + bx + c or a(x  h)^{2} + k or 2x^{2} 3x + 5 or 4x^{2}  1 or 3x^{2} + 2x 6. 
Uses of Quadratics

THE Quadratic Equation VS. A Quadratic Equation The equation ax^{2} + bx + c = 0 is the quadratic equation and its solution is . See page The Quadratic Equation, Formula, & Discriminant. The equation y = ax^{2} + bx + c is a quadratic equation because its highest degree is 2. It's an equation where a, the coefficient of the quadratic or x^{2} term, does not equal zero. If a were 0, there would be no quadratic term. It's an equation or statement in which y is expressed in terms of a, b, c, and x. Because it's a quadratic, the graph of the curve is a parabola, a quadratic function. Quadratic functions are the second simplest of the polynomial functions.
In general polynomials look like y = a_{n}x^{n} + a_{n1}x^{n1} + a_{n2}x^{n2} + ... +a_{2}x^{2} + a_{1}x^{1} + a_{0}x^{0}. These equations are quadratic: y = ax^{2} + bx + c or y = a(x  h)^{2} + k. 
Related Pages & Resources

www.mathnstuff.com/math/spoken/here/2class/320/c32pg00.htm 