Completing Squares

Completing Squares.

Moving Standard form to Vertex Form

y= ax^2 +bx+c y= a(x-h)^2 +k

We have learnt so far converting Vertex Form to Standard form simply by expanding. However, we have to work backwards, instead of expanding or simplifying, we will be factoring.

The only difference between Vertex form and Standard form is that the Vertex form has a "bracket squared" . This process is called COMPLETING THE SQUARES.

Example; (2x^2 + 4x) +5

1st Step: Group the first two terms and common factor. (DO NOT FACTOR OUT THE VARIABLES) because "ax^2" needs to be positive.

= 2(x^2+4x)+5

2nd Step: In the bracket, add and subtract the c value to make it a perfect square.

= 2(x^2 + 4x +4 -4) +5

3rd Step: Remove the negative C value by multiplying it to the number in front of the bracket.

= 2(x^2 + 4x +4)+ 2(-4) +5

4th Step: Factor the brackets to a perfect square.

= 2 (x+2) ^2 -3

So you will notice your answer will be in vertex form.