Question

The arch of the Sydney Harbor Bridge is appropriate 500 meters long and 85 meter high. What quadratic function models the curve of the arch? Assume the arch starts at (0,0).

Answer 1

Equation of arch, y= (-1.36 * 10⁻³)x²+0.68 x

Step-by-step explanation:

General form of quadratic equation is y = ax²+bx+c

The starting point is (0,0)

0 = a * 0² + b * 0 + c

c = 0

So y = ax²+bx

The ending point of arch is (500,0), since the length of arch is 500 m.

0 = a* 500² + b * 500

500 a + b = 0 -------------------------Equation 1

The mid point of arch is (250, 85), since the height of arch is 85 m.

85 = a * 250² + b * 250

12500 a + 50 b = 17 -------------------------Equation 2

Equation 1 x 50,

50*( 500 a + b) = 50*0

25000 a + 50 b = 0 -------------------------Equation 3

Equation 3 - Equation 2

25000 a + 50 b - ( 12500 a + 50 b) = 0 - 17

12500 a = -17

a = -1.36 x 10⁻³

Substituting in equation 1,

500 x (-1.36 x 10⁻³)+ b = 0

b = 0.68

So equation of arch, y= (-1.36 * 10⁻³)x²+0.68 x