Quandaries
and Queries 

Teresa (mother) A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the centre of the arch 

What you have here is an upside down parabola. Parabola are functions that have the form f(x) = ax^{2}+bx+c. In your case you may assume the parabola passes through the point (0,80)  the apex  and the two points (100,0) and (100,0)  we'd say f(x) has roots of x = 100 and x = 100. From this information you need to solve for a, b and c and find f(40). For example we can find c easily because f(0) = c but we know also f(0) = 80 so c = 80. Knowing that this parabola is symmetrical about the y axis tells us we can find be easily too. What is it? Good luck with the rest of it, 

