N2014 P1 Q4

The diagram shows the curve \(y=f(x)\), which crosses the \(x\)-axis at \(A\), \(B\) and \(C\), and has a maximum point at \(D\), where it crosses the \(y\)-axis. The coordinates of \(A\), \(B\), \(C\) and \(D\) are \((-a,0)\), \((b,0)\), \((c,0)\) and \((0,d)\) respectively, where \(a\), \(b\), \(c\) and \(d\) are positive.

1. Sketch the curve \(y^2=f(x)\), stating in terms of \(a\), \(b\), \(c\) and \(d\) the coordinates of any turning points and of any points where the curve crosses the \(x\)-axis.[4]
2. What can be said about the tangents to the curve \(y^2=f(x)\) at the points where it crosses the \(x\)-axis?[1]