Explain the steps necessary to convert a quadratic function in standard form to vertex form.

Answer:

To convert a quadratic function from standard form to vertex form, you use the process of completing the square. First, focus on the first two terms (the x^2 and x terms). Create a perfect square trinomial by adding a zero pair. The value of this pair is found by taking half of the coefficient of the x-term and squaring it. One value is added to form the perfect square trinomial, which is then rewritten as a squared binomial, while the other value is combined with the original constant term outside of the binomial.