a parabolic shaped shaped bridge is 30m wide. the height of the bridge is y=5m x=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, which is given by the equation:
y = a(x-h)^2 + k
where (h, k) represents the coordinates of the vertex.
Given that the bridge is 30m wide, we have two points to consider: (0, 0) at the edge of the bridge on the ground, and (8, 5) at a distance of 8m from the edge.
Plugging in the values of (h, k) = (8, 5) into the equation, we get:
0 = a(0-8)^2 + 5
0 = 64a + 5
64a = -5
a = -5/64
So, the equation that models the bridge is:
y = (-5/64)(x-8)^2 + 5
b) To find the maximum height of the bridge, we can observe that the vertex of the parabola represents the highest point. The vertex is given by the coordinates (h, k).
From the equation y = (-5/64)(x-8)^2 + 5, we can see that (h, k) = (8, 5).
Therefore, the maximum height of the bridge is 5 meters.