Start with the standard form: (y = ax^2 + bx + c)
Factor out (a) from the quadratic and linear terms: (y = a(x^2 + frac{b}{a}x) + c)
Complete the square inside the parentheses
Take half of the (x)-coefficient, square it, and add and subtract that value inside the parentheses
Rewrite the expression as a perfect square trinomial
Simplify to get vertex form: (y = a(x-h)^2 + k)
Identify (h) and (k) from the simplified equation
Use (h = -frac{b}{2a}) if needed
Use (k = f(h)) if needed