Question

The arch of a train tunnel is in the shape of a parabola. The maximum height of the tunnel is 20 m. If the origin of a grid is placed at one end of the arch where the tunnel contacts the road, the other point of contact with the road is 40 m away. Which quadratic function can be used to model the arch?

Answer 1

pfft! we don't need no steekin' answers to figure this out.

Answer 2

A parabola is symmetrical about the vertex, so the high point of the arch (aka the vertex) is 1/2 of the way between 0 and 40. That means the vertex is at (20,20).

Answer 3

well the line of symmetry is x = 20

and the point (20, 20) is the vertex

so the equation is

y =a(x(x-40)

or

y = a(x^2 - 40x)

sunstitute (20, 20) to find the value of a

20 = a(20^2 - 40(20))

20 = -400a

solve for a and then substitute into

y = a(x^2 - 40x)

Answer 4

thanks!