- #1

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y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

ax^2=3x^2 -----> a=3

-2ahx=-2x

-2(3)hx=-2x ----->h=1/3

K=----->-1

Therefore:

y=3(x-1/3)^2-1

But I think it's suppost to be: y=3(x+1/3)^2-4/3

Is that right??? So what is wrong....

- Thread starter thomasrules
- Start date

- #1

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y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

ax^2=3x^2 -----> a=3

-2ahx=-2x

-2(3)hx=-2x ----->h=1/3

K=----->-1

Therefore:

y=3(x-1/3)^2-1

But I think it's suppost to be: y=3(x+1/3)^2-4/3

Is that right??? So what is wrong....

- #2

- 335

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There's nothing wrong with your method...except that I find it very confusing!thomasrules said:

y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

ax^2=3x^2 -----> a=3

-2ahx=-2x

-2(3)hx=-2x ----->h=1/3

K=----->-1

Therefore:

y=3(x-1/3)^2-1

But I think it's suppost to be: y=3(x+1/3)^2-4/3

Is that right??? So what is wrong....

I know you are trying to compare terms to find h and k here, but how did the 2x get a negative sign?I want to put

y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

I'd recommend looking at it like this:

[tex]y=3x^2+2x-1[/tex]

[tex]y=3x^2+2x+D-D-1[/tex]

Now, a perfect square in the form [tex]a(x-h)^2[/tex] looks like:

[tex]ax^2-2ahx+ah^2=3x^2+2x+D[/tex]

We see that -2ah=2 and ah^2=D.

We of course know what a is, right? I leave it to you to finish finding h and D.

Then you've got:

[tex]y=(3x^x+2x+D)-D-1[/tex]

[tex]y=a(x-h)^2-D-1[/tex]

with whatever D value you have.

-Dan

- #3

mathman

Science Advisor

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In going from the first line to the second, it looks quite screwed up.y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

- #4

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Btw ya that was a mistake with the -2 , what should have bee +2

- #5

HallsofIvy

Science Advisor

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This is where you went wrong: you wantthomasrules said:Ok so can you please tell me where I go wrong here. I want to put

y=3x^2+2x-1 into y=a(x-h)^2+K

ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1

[tex]ax^2- 2ah+ ah^2+ k= 3x^2- 3x-1[/tex]

not "ah

No, ahax^2=3x^2 -----> a=3

-2ahx=-2x

-2(3)hx=-2x ----->h=1/3

K=----->-1

Therefore:

y=3(x-1/3)^2-1

But I think it's suppost to be: y=3(x+1/3)^2-4/3

Is that right??? So what is wrong....

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