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Write p(x)=3x^2+4x-1 in p (x)=a(a-h)^2+k form using complete the square method

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2 Answers

p(x) = 3x2 + 4x -1
p(x) - a(a-h)2 - k  ( think you mean p(x) = a(x+d)2 + e
 
Since in our eqn  the coefficient of the x2 term is not 1, we need to divide out the 3 by multiplying by 3/3
 
p(x) = (3x2 + 4x - 1)3/3
p(x) = 3( x2+ 4x/3 - 1/3)
 
now focusing on the 4x/3 term, if we divide the coeffieceint of that term 4/3 by 2 we get 2/3
squaring it we get (2/3)2 = 4/9  which is not = to -1/3
 
if we add and subtract the 4/9 to the our equation with in the parathesis we are keeping it the same eqn
 
p(x) = 3(x2 + 4x/3 +4/9 -1/3 - 4/9)
p(x) = 3[(x2+4x/3 +4/9) -1/3 -4/9]
 
not x2+4x/3 +4/9 can be written as (x+2/3)2
 
p(x) = 3[(x+2/3)2 - 3/9 -4/9]
p(x) = 3[(x+2/3)2 - 7/9]
 
not totally in the form yet, we need to remove the -7/9 term from the paranthesis. Do this by multiplying by the 3 using distributive property
 
p(x) = 3(x+2/3)2 -3(7/9)
p(x) = 3(x+2/3)2 -7/3

3x^2 + 4x -1 = 3(x^2 + 4x/3 - 1/3) = 3(x^2 + 4x/3 + 4/9 - 7/9) = 3(x + 2/3)^2 - 3(7/9) =

3(x + 2/3) - 7/3

Comments

You forgot to put the square sign after the (x + 2/3):
 
3 (x + 2/3)2 - 7/3
 
Instead of p(x) = a(a-h)2 - k, I think you meant to say p(x) = a(x-h)2 + k.
 
If p(x) = a(a-h)2 that would give you a3 + ah2 which is something else entirely.

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