SOLUTION: A bridge uses a parabolic arch to support it as shown in the picture. The bridge is 100 m long and has a maximum height of 75m. Determine an algebraic expression, in standard f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A bridge uses a parabolic arch to support it as shown in the picture. The bridge is 100 m long and has a maximum height of 75m. Determine an algebraic expression, in standard f      Log On


   

Question 324138: A bridge uses a parabolic arch to support it as shown in the picture. The bridge is 100 m long and has a maximum height of 75m.
Determine an algebraic expression, in standard form, that models the shape of the bridge.
If you must drive 10 m on the bridge before you reach the arch, how high is the bridge above the water below ?
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
There is no picture, so I will try to extrapolate.
Center it at the origin. The parabola representing the bridge arch passes through (50,0) and (-50,0) and has its vertex at (0,75).
We can use the equation y=a%28x-h%29%5E2%2Bk to model the parabola.
Plug in the given points and solve for a.
0=a%2850-0%29%5E2%2B75
0=a%2A2500%2B75
a=-75%2F2500=-3%2F100
Therefore, the parabola equation is
y=-3%2F100%2Ax%5E2%2B75
To find how high it is at a point, simply plug in the corresponding x value.
i.e. How high is the arch at x=25?
-3%2F100%2A%2825%29%5E2%2B75=56.25 m