A community for students.
Here's the question you clicked on:
 0 viewing
FreeTrader
 3 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
 3 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?

This Question is Closed

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

FreeTrader
 3 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
 3 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
 3 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.