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June 27th, 2015, 10:34 PM   #1
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Transformation

I used -b/2(a) for x and f(-b/2(a)) for y. I know I have to figure out by factoring or whatever to state for the basic function and how it's going to shift.

Problem: f(x) = 2x^2 - 4x + 1

How I solved it: -(-4)/2(2) then 4/4 then x = 1 for y I plugged in 1
y = f( 2(1)^2 - 4 (1) + 1 )
y = f( 2 - 4 + 1 )
y = -1

My attempt to solving it by factoring:
A) basic function y = x^2
(0,0), (1,1), (-1,1) (for basic plot of parabola)
B) then I factor the f(x) = 2 (x^2 - 2x) + 1 <- this is where I'm stuck at
but the book answer was f(x) = 2(x - 1)^2 - 1

I know this is basic algebra, please help so I can do this transformation.

another similar problem where I'm pulling my hair out is
f(x) = 1/2(x)^2 + x - 1
(same transformation problem)

Last edited by skipjack; June 28th, 2015 at 12:08 AM.
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June 28th, 2015, 12:13 AM   #2
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This isn't so much a transformation as just finding the vertex.

I'll start where you left off:

\begin{align*}
&\quad\,\,2(x^2 - 2x) + 1\\
&= 2(x^2 - 2x + 1 - 1) + 1\\
&= 2(x^2 - 2x + 1) - 1\\
&= 2(x - 1)^2 - 1
\end{align*}

See if you can carry on with the second problem now.
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June 28th, 2015, 12:39 AM   #3
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Instead of -b/2(a), write -b/(2a).

As a = 2 and b = -4, -b/(2a) = 4/(4) = 1, and f(1) = -1 is correct.

There is no need to try to factor!

The rule is that ax² + bx + c ≡ a(x + b/(2a))² - b²/(4a) + c.

Putting in a = 2, b = -4 and c = 1 gives 2x² - 4x + 1 ≡ 2(x - 1)² - 2 + 1 ≡ 2(x - 1)² - 1.
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June 28th, 2015, 03:06 PM   #4
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The book asks by using transformation

I know I'm making my life harder but I need to know how to do it so I can perform in testing condition
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June 28th, 2015, 03:06 PM   #5
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Quote:
Originally Posted by Azzajazz View Post
This isn't so much a transformation as just finding the vertex.

I'll start where you left off:

\begin{align*}
&\quad\,\,2(x^2 - 2x) + 1\\
&= 2(x^2 - 2x + 1 - 1) + 1\\
&= 2(x^2 - 2x + 1) - 1\\
&= 2(x - 1)^2 - 1
\end{align*}

See if you can carry on with the second problem now.
Thank you so much, I still don't get it but I'm going to study it till my head explodes.

Seriously thank you so much
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