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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

I need help on my homework. College algebra.

### 2 Answers by Expert Tutors

Felice R. | Need Help in Math and Science - Engineer willing to helpNeed Help in Math and Science - Engineer...
4.0 4.0 (1 lesson ratings) (1)
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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
4.9 4.9 (220 lesson ratings) (220)
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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