Quandaries and Queries


Teresa (mother)
Grade 11 student Robyn

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 up-side down parabola. Parabola are functions that have the form f(x) = ax2+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,


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