Determine the real values of ( a, b ), and ( c ) for the quadratic function ( f(x)=a x^{2}+b x+c, a neq 0 ) that satisfy the conditions ( f(0)=0 ), ( lim _{x rightarrow-1} f(x)=3 ), and ( lim _{x rightarrow 2} f(x)=6 ). Explain all steps of the solution. [T 6]

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Determine the real values of  ( a, b  ), and  ( c  ) for the quadratic function  ( f(x)=a x^{2}+b x+c, a  neq 0  ) that satisfy the conditions  ( f(0)=0  ),  (  lim _{x  rightarrow-1} f(x)=3  ), and  (  lim _{x  rightarrow 2} f(x)=6  ). Explain all steps of the solution. [T 6]

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(Solved): Determine the real values of \( a, b \), and \( c \) for the quadratic function \( f(x)=a x^{2}+b x ...

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