# 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.

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

$\\ \\ \Rightarrow \hspace{1cm}f(0)=5=a\cdot 0^{2}+b\cdot 0+c\\ \\ \Rightarrow \hspace{1cm}f(-1)=10=a-b+c\\ \\ \Rightarrow \hspace{1cm}f(1)=a+b+c.$

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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