Question

2. The cable of a suspension bridge hangs in the shape of a parabola. The
towers supporting the cable are 400 ft apart and 150 ft high. If the cable,
at its lowest, is 30 ft above the bridge at its midpoint, how high is the cable
50 ft away (horizontally) from either tower?
(200, 150)​

Answer 1

Answer:

= 0, y = 20

x = -600, y = 170

x = +600, y = 170

using the form ax^2 + bx + c = y, we know that c=20

x=-600, y = 170 and x =+600, y = 170; write two equations

-600^2a - 600b + 20 = 170

+600^2a + 600 + 20 = 170

use elimination

360000a - 600b + 20 = 170

360000a + 600b + 20 = 170

------------------------------addition eliminates b

720000a + 40 = 340

720000a = 300

a = 300/720000

a = .0004167

Now we can write the equation

y = .0004167x^2 + 20

Graphically

Step-by-step explanation:

Hope I help you!!