N2011 P1 Q2

It is given that \(f(x)=ax^2+bx+c\), where \(a\), \(b\) and \(c\) are constants.

1. Given that the curve with equation \(y=f(x)\) passes through the points with coordinates \((-1.5,4.5)\), \((2.1,3.2)\) and \((3.4,4.1)\), find the values of \(a\), \(b\) and \(c\). Give your answers correct to 3 decimal places.[3]
2. Find the set of values of \(x\) for which \(f(x)\) is an increasing function.[2]