- #1

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the curve C has the equation y=x

^{2}+ 2x + 4

a) Express x

^{2}+2x + 4 in the form a(x+b)

^{2}+ c and hence the coordinates of the minimum point C.

This is what i've done:

x

^{2}+2x +4 = a(x+b)

^{2}+c

a(x+b)(x-b) + c = x

^{2}+2x+4

a(x

^{2}+ xb+ xb +b

^{2}) + c = x

^{2}+2x+4

ax

^{2}+ 2abx + ab

^{2}+ c = x

^{2}+2x+4

Therefore: a= 1, 2ab= 2, ab= 1, b= 1, ab

^{2}+ c= 4

1+c = 4

c= 3

(x=0) y= 4

y= 1(x+1)

^{2}+ 2

..and that's all i've got so far. Please let me know if it's all wrong and how do i go about getting the minimum point from here.

Thanks!