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secondary 4 | A Maths

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Challenging question for functions.

y = ax² + bx + c

In this case, since we are measuring x from the centre, , the midpoint of the curve is on the y axis. So the value of b is 0.

Lowest height of the cable = 80m.

At the centre, x = 0, then y = c .

Since lowest height is 80m, c = 80.

If the two 200m-high towers are 1200m, then distance from the centre to either tower is half of it

= 600m

This also tells you that

y = 200 when x = 600 or -600

We can now come up with the following :

y = ax² + 80

Sub y = 200, x = 600(or -600, up to you)

200 = a(600²) + 80

200 = 360000a + 80

120 = 360000a

a = 120/360000

a = 1/3000