A parabolic 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.