create an equation for the parabola for sydney harbour bridge with the height of 440 ft and distance between towers is 1,650 ft

Answer 1

y = f(x) = Ax^2 + Bx + C is the quadratic function

(0,0) <--- left endpoint of the bridge

(1650,0) <--- right endpoint of the bridge

1650/2 = 825

(825, 440) <--- this is the vertex

(0,0) ---> C=0

So the quadratic function becomes

y = f(x) = Ax^2 + Bx

0 = A(1650)^2 + 1650B = 2722500A + 1650B

440 = A(825)^2 + (825)B

440 = 680625A + 825B

The two equations are:

0 = 2722500A + 1650B

440 = 680625A + 825B

Multiplies second equation by -4 and adds it to the first equation:

-1760 = -1650B

B = -1760/-1650 = 176/165 = 16/15

Per the first equation: 0 = 2722500A + 1650(16/15)

0 = 2722500A + 1760

A = -1760/2722500 = -160/247500

= -16/24750

= -8/12375

y = f(x) =( -8/12375)x^2 + (16/15) x