Question

A parabolic bridge over a river is 30.0 m wide and 12.0 m high. Find the equation, in factored form, that represents the parabolic arch of the bridge.
struggling please help with this

Answer 1

since the bridge is 30m wide, its highest point is at (0,12)
set it up as y = 12 - ax^2
where y(15) = 0

or, you could start with y = a(x-15)(x+15)
where y(0) = 12

Answer 2

You're given the y-coordinate of the vertex (__, 12), but the x-coordinate is missing. However, that can easily be calculated by determining the
midpoint of 0 and 30 (15). This is the best way I can visually explain it (imagine the arch being drawn).

12 |
|
|___________________
0 15 30

This can be expressed in factored form:
y= a(x-0)(x-30)
y= ax(x-30)

Since we have our vertex/another point, you can calculate further to determine the value of a.

12= a(15)(15-30)
12= a(15)(-15)
12= -225a
-12/225 = a

The complete equation is now: y= -12/225(x)(x-30)

Answer 3

The visual representation kind of messed up...

12|
. |
. |_________________
. 0. 15. 30