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MTH 163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
A Humble Inquiry
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http://vhcc2.vhcc.edu/pc1fall9/homepage_163_menu_driven.htm
f(x) Notation; The Generalized Modeling Process <- <- <-
Examples of the f(x) notation <- <-
Replacing the variable by an algebraic expression <-
This expression can be simplified as follows:
f(x-5) =
3(x-5)^2 + 2(x-5) - 4 =
3 [(x-5)(x-5)] + 2(x-5) - 4 = `
3 [x(x-5) - 5(x-5)] + 2(x-5) - 4 =
3[x^2-5x - 5x+25] + 2x-10 - 4 =
3[x^2 - 10x + 25] + 2x-10 - 4 =
3x^2 - 30x + 75 + 2x-10 - 4 =
3x^2 - 28x + 71.
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Following the example, I had completed as follows:
f(x) = 3x^2 + 2x - 4 for when f(x-5)= 3(x-5)^2 + 2(x-5) - 4.
= 3[ (x-5)(x-5)] + 2(x-5) - 4
= 3[x(x-5)-5(x-5)] + 2(x-5) - 4
= 3( x^2 - 5x - 5x + 25 ) + 2x - 10 - 4
= 3x^2 - 15x - 15x + 75 + 2x - 10 - 4
= 3x^2 -30x + 75 + 2x - 14
= 3x^2 - 28x + 61
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My specific inquiry is that I'm unsure how my solution, 3x^2 - 28x + 61, differs from your solution, 3x^2 - 28x + 71.
Any help you provide will be welcomed and appreciated.
self-critique #$&*
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The difference appears to be that in my solution I overlooked the -10 when simplifying from
3x^2 - 30x + 75 + 2x-10 - 4
to
3x^2 - 28x + 71.
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Your solution appears to be correct.
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