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Quick math question

Find values for the constants a, b, and c that will make
f(x)=cos x and g(x)=a+bx+cx^2
satisfy the following conditions:
f(0)=g(0)
f'(0)=g'(0)
f''(0)=g''(0)

I get the basic set up, I am just ending up with 2 possible scenarios. Not sure if this is the correct way to do it. But so far I have

1=a
0=b+2x(c)
pi/2 or 3pi/2=2c

and I'll just have 2 scenarios for my system of equations?

July 17, 2012