Find a function of the form f(x)=ax^2 +bx+c , if it is know that f(0)=5;f(-1)=10;f(1)=6.

Answers (1)

Solution:    We have ,  f(x)=ax^2+bx+c

            \ \ Rightarrow hspace1cmf(0)=5=acdot 0^2+bcdot 0+c\ \ Rightarrow hspace1cmf(-1)=10=a-b+c\ \ Rightarrow hspace1cmf(1)=a+b+c.

Determine the coefficient  a,b,c  from the above system . we have 

   a=3;b=-2;c=5      Hence      f(x)=3x^2-2x+5.

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