Start with the standard form: (y = ax^2 + bx + c)

Factor out (a) from the (x^2) and (x) terms if (a neq 1): (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 expression

Rewrite the trinomial as a perfect square

Simplify to get vertex form: (y = a(x - h)^2 + k)

Use (h = -frac{b}{2a}) and (k = f(h)) if needed