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FreeTrader
 4 years ago
Problem Set 1 Question 1A1 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 slopeintercept form but my answer is different from the Solution. Help?
FreeTrader
 4 years ago
Problem Set 1 Question 1A1 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 slopeintercept form but my answer is different from the Solution. Help?

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LagrangeSon678
 4 years ago
Best ResponseYou've already chosen the best response.1you could have factored out a 3 from the begining

FreeTrader
 4 years ago
Best ResponseYou've already chosen the best response.1The answer for the slopeintercept 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?

FreeTrader
 4 years ago
Best ResponseYou've already chosen the best response.1I 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.

FreeTrader
 4 years ago
Best ResponseYou've already chosen the best response.1LagrangeSon678, 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 slopeintercept form, and it can be sketched readily.
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