identity of two quadratic expression 2 unit year 11 (1 Viewer)

[Thatstudentm9]

question:
express the following quadratic polynomial in the form a(x+b)^2+c

these are the steps i've attempted


x^2-4x+6=a(x^2+2xb+b^2)+c


x^2-4x+6= ax^2 +2axb+ab^2+c

x^2-4x+6= ax^2+(2x+b)ab+c


i got stuck in finding the identities of a,b and c and can't do anything further

 

[pikachu975]

question:
express the following quadratic polynomial in the form a(x+b)^2+c

these are the steps i've attempted


x^2-4x+6=a(x^2+2xb+b^2)+c


x^2-4x+6= ax^2 +2axb+ab^2+c

x^2-4x+6= ax^2+(2x+b)ab+c


i got stuck in finding the identities of a,b and c and can't do anything further

Note that x^2 - 4x + 4 = (x-2)^2
Hence x^2 - 4x + 4 +2 = (x-2)^2 + 2

You can also complete the square, (x-2)^2 + 6 - 4 = (x-2)^2 + 2