Quandaries
and Queries 

Francis Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly. height from base to highest point 45.75
centimetres


Hi Francis, You didn't send us a diagram so I guessed at the diagram below. I changed all the dimesnions to centimeters. I put a coordinate system on the diagram (the axes are in yellow). Since the shape of the crosssection is a parabola, and in my diagram the parabola has its axis on the Yaxis and opens downward, the equation of the parabola is y = a x^{2} + b where a is positive. The points (0, 45.75) and (2500, 0) are on the parabola so they satisify the equation. Substitute the two points into the equation and you will get two equations in a and b. Solve these equations to find a and b and then you will have the equation of the parabola. Harley 

