Question 29361: How do you expand an equation into general form such as y=2(x+3)^2-8
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! How do you expand an equation into general form such as y=2(x+3)^2-8
y=2(x+3)^2-8 ----(1)
(y+8) = 2(x+3)^2
Squaring both the sides
(y+8)^2 = [2(x+3)^2]^2
y^2+16y+64 = 2^2 [(x+3)^2]^2
(using (a+b)^2 = a^2 +2ab+b^2 formula on the LHS where a = y and b = 8)
And using (mn)^2 = (m^2)(n^2) on the RHS
y^2+16y+64 = 4[(x^2+6x+9)]^2
(using (a+b)^2 = a^2 +2ab+b^2 formula on the RHS where a = x and b = 3)
y^2+16y+64 = 4[x^4+36x^2+81+12x^3+108x+18x^2]
(using (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca where here a=(x^2),b=(6x) and c=9 )
y^2+16y+64 = 4[x^4+12x^3+54x^2+108x+81]
(grouping like terms and writing in descending powers of x)
y^2+16y= 4[x^4+12x^3+54x^2+108x]+ [4X81]-64
4(x^4)+48(x^3)+216(x^2)+432(x)-(y^2)-16(y)+260 = 0
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