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