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I'm a bit stuck on this question:
the curve C has the equation y=x2 + 2x + 4
a) Express x2 +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:
x2 +2x +4 = a(x+b)2+c
a(x+b)(x-b) + c = x2+2x+4
a(x2 + xb+ xb +b2) + c = x2+2x+4
ax2 + 2abx + ab2 + c = x2 +2x+4
Therefore: a= 1, 2ab= 2, ab= 1, b= 1, ab2 + 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!
the curve C has the equation y=x2 + 2x + 4
a) Express x2 +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:
x2 +2x +4 = a(x+b)2+c
a(x+b)(x-b) + c = x2+2x+4
a(x2 + xb+ xb +b2) + c = x2+2x+4
ax2 + 2abx + ab2 + c = x2 +2x+4
Therefore: a= 1, 2ab= 2, ab= 1, b= 1, ab2 + 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!