Problem Set 1 Question 1A-1 b)
By completing the square, use translation and change of scale to sketch:
y = 3x^2 + 6x +2

Here is the method I attempted, but with a different result than shown in the Solutions. Where am I going wrong?

y = 3x^2 + 6x +2
y - 2 = 3x^2 + 6x [move 2 to the left side]
y - 2 = 3(x^2 +2x) [factor out 3]
y - 2 +1 = 3(x^2 +2x +1) [complete the square]
y - 1 = 3(x +1)^2 [rearrange toward slope - intercept form]
y = 3(x+1)^2 +1 [add one to both sides]

Now, I have it in slope-intercept form but my answer is different from the Solution. Help?

Question

Problem Set 1 Question 1A-1 b)
By completing the square, use translation and change of scale to sketch:
y = 3x^2 + 6x +2

Here is the method I attempted, but with a different result than shown in the Solutions.  Where am I going wrong?

y = 3x^2 + 6x +2
y - 2 = 3x^2 + 6x    [move 2 to the left side]
y - 2 = 3(x^2 +2x)   [factor out 3]
y - 2 +1 = 3(x^2 +2x +1)   [complete the square]
y - 1 = 3(x +1)^2    [rearrange toward slope - intercept form]
y = 3(x+1)^2 +1  [add one to both sides]

Now, I have it in slope-intercept form but my answer is different from the Solution.  Help?

anonymous · Answer

you could have factored out a 3 from the begining

anonymous · Answer

The answer for the slope-intercept form given by the Solutions set is different from mine, 
it is $$y=3(x+1)^{2}-1$$

The last number I got was +1, but the key says -1.  Am I doing something wrong?

anonymous · Answer

I now see that in step 4, when I completed the square, I should add 3 to the left side due to the 3 distribution on the 1 on the right side.  This results in a solution that matches the answer key, and is equivalent to the original equation when substituting in various values for x.  Thanks to Throol, who addressed this in another forum.

anonymous · Answer

LagrangeSon678, you are right.  Dividing out the 3 on the right side also would work, and would eliminate the need to distribute the three over the added 1 on the right.  As follows:

1) Original Equation:  $$y=3x ^{2}+6x+2$$ 
2) Divide out 3 from Right Side:  $$y/3 = x^2 +2x + 2/3$$
3) Subtract 2/3 from both sides:  $$y/3 -2/3 = x^2 +2x$$
4) Complete the Square:  $$y/3 -2/3 + 1 = x^2 +2x +1$$
5) Get Common Denominator on Left Side:  $$y/3 -2/3 + 3/3 = x^2 +2x +1$$
6) Simplify Left Side: $$ y/3 + 1/3 = x^2 +2x +1$$
7) Factor Right Side: $$ y/3 + 1/3 = (x+1)^2$$
8) Multiply by 3 on both sides:  $$y +1 = 3(x+1)^2$$
9) Subtract 1 from both sides:  $$y = 3(x+1)^2 - 1$$

And now we have the equation in slope-intercept form, and it can be sketched readily.