How are quadratic equation in standard form rewritten in vertex form?

A quadratic equation in standard form, ( ax^2 + bx + c ), can be rewritten in vertex form, ( a(x-h)^2 + k ), through the process of completing the square. First, factor out ( a ) from the ( x^2 ) and ( x ) terms, then manipulate the equation to create a perfect square trinomial inside the parentheses. The vertex ( (h, k) ) can be found from the values derived during this process, specifically ( h = -\frac{b}{2a} ) and ( k ) can be calculated by substituting ( h ) back into the original equation.