Question

The path of a rope bridge can be modeled by a quadratic equation h(l) , where h is the height at a point on the bridge relative to the two ends of the bridge and l is the distance from one end of the bridge. One such bridge connects two ends that are 24 meters apart. The lowest point of the bridge is 3 meters lower than the two ends of the bridge.

Answer 1

Given : bridge connects two ends that are 24 meters apart. The lowest point of the bridge is 3 meters lower than the two ends of the bridge.

To Find : Equation

Solution:

h is the height at a point on the bridge relative to the two ends of the bridge and l is the distance from one end of the bridge

Ler say:

h = al^2 + bl + c

at l = 0 , h = 0

0 = 0 + 0 + c

c = 9

at l.= 24 , h = 0

0 = a(24)^2 + b(24) + 0

b = - 24a

at l = 12 h = -3

-3 = a(12)^2 + b(12) + 0

-3 = 144a - 288a

-3 = -144a

1 = 48a

a = 1/48

b = -1/2

h = l^2/48 - l/2

Learn More:

The red parabola shown is the graph of the equation x = ay^2 + by + ...

brainly.in/question/18271901

Find the equation of the parabola that satisfies the following ...

brainly.in/question/17176081