# 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 = 2x`

^{2} - 8x + 17

Group the first two terms:

`y = (2x`

^{2} - 8x) + 17

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

`y = 2(x`

^{2} - 4x) + 17

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

`y = 2(x`

^{2} - 4x + 4 - 4) + 17

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

`y = 2(x`

^{2} - 4x + 4) + 17 - 8

`y = 2(x`

^{2} - 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)