Thread: I have a problem solving question and similar to Todd im into the conics section.

1)A section of roller coaster track is in the shape of a parabola. The track spans a horizontal distance of 84 yards and has a maximum height of 32 yards. Six vertical support beams are located at a a distance of 12 yards from each other. Find the sum of the lengths of all six vertical support beams.

Originally Posted by chris28

1)A section of roller coaster track is in the shape of a parabola. The track spans a horizontal distance of 84 yards and has a maximum height of 32 yards. Six vertical support beams are located at a a distance of 12 yards from each other. Find the sum of the lengths of all six vertical support beams.

1. Define a coordinate system. I suggest the origin to be the midpoint of the horizontal distance.

2. Then the general equation of the parabola is

p(x) = a x^2+32

3. You know the coordinates of V(0, 32) and B(42, 0). Plug in the coordinates of B into the equation of the parabola:

0 = a*(42)² + 32 ==> a = - 8/441

The complete equation is : p(x) = -8/441 * x^2 + 32

4. To use 6 vertical beams you have to divide the horizontal span into 7 equal distances (why?). Make a table and calculate p(-30), p(-18), ... p(30). For symmetry reasons you only have to calculate 3 values.