Question

prove that, g(a2)=g(a-2)​

Answer 1

Answer:

The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.

Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.

How high is the cable 120m away from a tower? Sketch the graph.

:

lets have the bridged centered at the origin

Three points are needed on the parabola

x = 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

+graph%28+300%2C+200%2C+-700%2C+700%2C+-100%2C+200%2C+.0004167x%5E2%2B20%2C+170%2C+116%29+

:

"How high is the cable 120m away from a tower? "

600 - 120 = 480

Solve for x=480

y = .0004167(480^2) + 20

y = 96 + 20

y = 116 m high (blue line)