Question y=3x² -12x + 7

Question

Hello, I did this question from my homework and got it slightly wrong. I checked it over multiple times but still don't know what I screwed up.

Question y=3x² -12x + 7 Complete the Square

Here is what I did:

I used the formula -b/2a to figure out what x is. Here -b/2a is -1x-12/2x3 which is 12/6. 12÷6=2 so x=2. Then I plugged it in.

y=3(2)² -12(2) + 7

y=12 -24 +7

y=-5

Now that I had x and y I put it into vertex form, how the answers are supposed to appear.

y= 3(x-2)²-5 My final answer.

The answer in the book was y= 3(x-2)²+3

What did I do wrong?

Answer 1

Personally, I never learned how to Complete the Square using -b/2a. I solved it on my own and got the same thing that you did.

y = 3x² - 12x + 7

y/3 = x² - 4x + 7/3

y/3 - 7/3 = x² - 4x

y/3 - 7/3 + 4 = x² - 4x + 4 , in this method you want to add (b/2)² to both sides because that will factor the trinomial down to (x+(b/2))²

y/3 + 5/3 = (x-2)²

y/3 = (x-2)² - 5/3

y = 3(x-2)² - 5

I'm 99.9% sure it's a typo in the textbook. Trust me, it happens :)

It's always a good feeling to get a math question right when even the ones who wrote the textbook didn't.

Answer 2

y = 3x² - 12x + 7

 

a = 3

b = -12

 

y - 7 = 3x² - 12x

 

Add b²/(4a) to both sides.

 

b²/(4a) = 144/[4(3)] = 12

 

y - 7 + 12 = 3x² - 12x + 12 = 3(x² - 4x + 4) = 3(x - 2)²

 

y + 5 = 3(x - 2)²

 

y = 3(x - 2)² - 5

Answer 3

You are correct up to the point of -b/2a = 2.

y = 3x² -12x + 7

y = 3(x² - 4x     ) + 7

y = 3(x² - 4x + 2) + 7 - 6  (6 what added in, it must be balanced out.)

y = 3(x² - 2)² + 1