Math Tutorial: Completing the Square

This tutorial demonstrates how to rewrite a general quadratic equation into vertex from by completing the square. As a math tutor I find that many students struggle with this concept. The example provided below is a fairly basic problem that most grade 11 math students should be able to solve proficiently.

Example:

Find the vertex of the quadratic equation:

y = 2x2 - 8x + 17

Group the first two terms:

y = (2x2 - 8x) + 17

Factor the first two terms inside the brackets if possible. This number is referred to as the leading coefficient:

y = 2(x2 - 4x) + 17

Add and subtract the square of half the coefficient of the second term inside the brackets (4/2)^2:

y = 2(x2 - 4x + 4 - 4) + 17

Remove the forth term from inside of the brackets to the outside multiplying by the leading coefficient:

y = 2(x2 - 4x + 4) + 17 - 8

y = 2(x2 - 4x + 4) + 11

Factor the trinomial inside of the brackets and express as a perfect square binomial:

y = 2(x - 2)2 + 11

The vertex of this equation is (2,11)