I'm a bit stuck on this question:(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Minimum Point

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