a parabolic shaped bridge is 30m wide. the height of the bridge is 5m 8m from the edge of the bridge.
a) what is the equation that models the bridge?
b) what is the maximum height of the bridge?
a) To find the equation that models the bridge, we can use the vertex form of a parabola equation. The vertex form of a parabola equation is given by y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
In this case, the vertex is at (0,5) because the bridge is symmetric and the highest point is in the middle. Thus, the equation that models the bridge is y = a(x-0)^2 + 5.
To find the value of 'a', we can use the information provided that the height of the bridge is 8m from the edge of the bridge. Plugging in these values into the equation:
8 = a(15)^2 + 5
b) To find the maximum height of the bridge, we need to find the vertex of the parabolic equation. The vertex occurs at the point (0,5) in this case, so the maximum height of the bridge is 5 meters.