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

In your fourth step, you've added 1 to the left side, but 3 to the right (3(+1), so the quantities are no longer equal.  Try adding 3 to both sides, and you should get what you're looking for :)

anonymous · Answer

$$y-2=3(x ^{2}+2x)$$
Next you'll add 3 to both sides:
$$y-2+3=3(x ^{2}+2x)+3$$
Factor out the 3,
$$y+1=3(x ^{2}+2x+1)$$
and take it from there.

anonymous · Answer

Thank you, Throol.  I see that your solution is equivalent to the original equation.