Aparabolic archway is 12 meters high at the vertex. at a height of 10 meters, the width of the archway is 8 meters. how wide is the archway at ground level?

To solve this problem you must apply the proccedure shown below:

 1. You have that the parabola is 12 meters high at the vertex and at a height of 10 meters, the width is 8 meter. 

 2. Therefore, you have:

 x^2=-4a(y^2-k)
 4^2=-4a(10-12)
 16=-40a+48
 16=8a
 a=16/8
 a=2

 y=0
 x^2=-8(0-12)
 x^2=96
 x=√96
 x=9.79x2
 x=19.58

 3. Therefore, as you can see, the answer is: 19.58 meters.