# Thread: Reversing the operation of completing the square

1. ## Reversing the operation of completing the square

I have; 3x^2 + 18x + 15. I end up with 3(x+3)^2 - 12. I understand how I did this and don't need any help getting through to the end as shown.

Now what I am asking help with is the reverse of the above.

This is the final line of completing the square; 3(x + 1)^2 - 12

If I expand the brackets and simplify I end up with; x + 3x - 11

I have a graphics calculator and when I enter; 3(x + 1)^2 - 12 the y intercept when x=0 is - 9 and not - 11 as shown?

My working out;

3(x + 1)^2 - 12

3(x + 1)(x + 1) - 12

3(x^2 + x + x + 1) - 12

3(x^2 + 2x + 1) - 12

3x^2 + 6x + 3 - 36

3x^2 + 6x - 33

x^2 + 3x - 11

If my graphic calculator is right could somebody please point out where I am going wrong!

Thanks

2. Originally Posted by Probability
I have; 3x^2 + 18x + 15. I end up with 3(x+3)^2 - 12. I understand how I did this and don't need any help getting through to the end as shown.

Now what I am asking help with is the reverse of the above.

This is the final line of completing the square; 3(x + 1)^2 - 12

If I expand the brackets and simplify I end up with; x + 3x - 11

I have a graphics calculator and when I enter; 3(x + 1)^2 - 12 the y intercept when x=0 is - 9 and not - 11 as shown?

My working out;

3(x + 1)^2 - 12

3(x + 1)(x + 1) - 12

3(x^2 + x + x + 1) - 12

3(x^2 + 2x + 1) - 12

3x^2 + 6x + 3 - 36 <<<<< This should be 3 * x^2 + 6 * x + 3 - 12

= 3 * x^2 + 6 * x - 9

Thus you have 'y-intercept' of '-9'

3x^2 + 6x - 33

x^2 + 3x - 11

If my graphic calculator is right could somebody please point out where I am going wrong!

Thanks
.

3. Originally Posted by Subhotosh Khan
.