Question 832026
Wow this one looks cool haha.
First, you need to know the standard form of parabola, which is {{{y=a(x-h)^2 + k}}}
And your vertex is always (h,k) 
When they tell you to write an equation for parabola with a word problem without given you the vertex, the vertex will automatically be (0,0) so your h will be 0 and your k will also be 0
Then you have {{{y = ax^2}}} and now you need to find the "a" in the equation
To find the a, you need at least 1 point on the parabola to find it.
Now you have to find the point (x,y)
Well, let's talk about the given info. 
The height is 180ft, that means you go up 180 from your vertex, that means your y is 180, then you have (x,180) is the point so far .
It says the bridge has a span of 600 feet, You know a parabola has a shape of a U with two sides exactly the same, one to the left and one to the right, right? 
This means you go to the left 300 and then go to the right 300, that will make it 600 :D, so your x will be either -300 or 300, doesn't matter which one you choose
So your point is (300,180) 
Now let's plug it in the equation.
{{{y = ax^2}}}
{{{180 = a*(300)^2}}}
{{{180 = 90000a}}}
{{{a = 180/90000}}}
{{{a = 1/500}}}
So your equation will be y = 1/500*x^2
TA-DAH
:D