Modelling the equation of a parabola.

Two parabolas are joined smoothly at the point B(30,20).

a) The parabola through A and B has a zero gradient at A(0,60). Find the equation of this parabola expressing all coefficients as exact values.

The general equation of a quadratic is:

Hence the equation of the parabola is:

Is this right so far? Can anyone confirm? Anybody got any ideas on how I'd go about answering b and c?

b) The parabola through B and C has a zero gradient at C. If the equation of this parabola is , find the exact values for a and p.

c) Write down the coordinates of this point.