The diagram below is of two parabola (ASD and BTD) joined together smoothly.

a) Find the value of y1.

Consider the points (27.5, 19.5)and (27,y1)

Is this correct? Sorry don't know how to use latex to make it all look neat.

b) Parabola BTD contains the point D and has a zero gradient. Show that its equation is

c) Use calculus to find the gradient of the parabola BTD at point 0.

d) Hence find the equation of the parabola ASD containing point A and joined smoothly to parabola BTD at point D. Curves joined smoothly at a point have the same gradient that that point.

Please keep any working out as simple as possible so that I can understand. Any help regarding these questions will be appreciated!