Final answer:
To model the parabolic bridge, we use the intercept form of the equation, y = a(x - p)(x - q). The x-intercepts are at -10 and 10, and the maximum height is 8 meters, which implies the vertex is at (0, 8). Calculating for 'a' using these values, we find the equation to be y = -0.08(x + 10)(x - 10).
Step-by-step explanation:
To determine the intercept form equation of the parabolical bridge, we can start by identifying the characteristics of a parabola in an intercept form, which is y = a(x - p)(x - q), where p and q are the x-intercepts of the parabola. Since the bridge is 20m wide, we can assume that the x-intercepts are at -10 and 10, because the parabola is symmetrical and the middle of the bridge (which is also the vertex of the parabola) will be at x=0. The maximum height of the bridge, which is 8m, occurs at the vertex. Knowing that the vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and the bridge's vertex is at (0, 8), we can write the equation as y = a(x - 0)^2 + 8. We just need to find the value of a. As the parabola passes through (10, 0), we can plug in these values to solve for a:
y = a(x^2)+8
0 = a(10^2) + 8
-8 = 100a
a = -0.08
Finally, the intercept form equation of the bridge is y = -0.08(x + 10)(x - 10).