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Functions, 2ADV EQ-Bank 13

\(f(x)=x^2-x,\ \ g(x)=a(x+3)^2+b x+c-1\)

Find the values of \(a, b\) and \(c\) if the quadratic functions \(f(x)\) and \(g(x)\) have the same graph.   (3 marks)

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\(a=1, \ b=-7, \ c=-8\)

Show Worked Solution
\(g(x)\) \(=a\left(x^2+6 x+9\right)+b x+c-1\)
  \(=a x^2+6 a x+9 a+b x+c-1\)
  \(=a x^2+(6 a+b) x+9 a+c-1\)

 

\(f(x)=x^2-x\)

\(\text{Since  \(f(x)=g(x)\), equating co-efficients:}\)

\(a=1\)

\((6+b)=-1 \ \Rightarrow \ b=-7\)

\(9+c-1=0 \ \Rightarrow \ c=-8\)