Asuspension footbridge has two 2-meter vertical supports 20 meters apart. the lowest point of the cable connecting them is 1 meter above the path. if the y-axis represents the left support what is the vertex form of the equation for the parabola describing the suspension cable?

The final equation is y = 0.01(x - 10)^2 + 1

Step-by-step explanation:

The vertex form of a parabola is given by f(x) = a(x - b)^2 + c, where (b, c) is the vertex of the parabola.

To find the vertex, it is given that " two 2-meter vertical supports 20 meters apart" and "The lowest point of the cable connecting them is 1 meter above."

The vertex will be at the mid-point between the two supports: b = 20/2 = 10m

It is 1m above so c = 1m

Substituting into f(x), y = f(x) = a(x - 10)^2 + 1

On the support 20m away from y-axis, x=20, y=2

2 = a(20 - 10)^2 + 1

1 = 100a

a = 0.01

The final equation is y = 0.01(x - 10)^2 + 1