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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?

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you could have factored out a 3 from the begining
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?
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.

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Other answers:

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.

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