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Question

Find a,b, c when f(x)=ax2+bx+c=0 and f(0)=6,f(2)=11,f(3)=6.
Determine f(x) to find the value of f(1).

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Solution

f(0)=a0+b0+c=6c=6f(3)=9a3b+6=69a=3b3a=bf(2)=4a+2b+6=114a+2b=54a+23a=5a=12

and b=32

Hence, f(x)=12x2+32x+6f(1)=12+32+6=8

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