Pre calc word problem Parabolic archway

[unrealmatt3]

Homework Statement

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?

Homework Equations

given in the picture it has (-4,10) and (4,10) along with vertex (0 ,12)

The Attempt at a Solution

(y- 12)^2 =4p(x - 0)

12 = 4p(0) p = 3 ?? I don't know if i need this

i have a picture but not sure what i need to do

 

[rl.bhat]

Hi unrealmatt3, welcome to PF.
Consider vertex as the origin.
The equation of the parabola becomes
y^2 = 4*p*x.
In the first position x = (12 - 10) and y = 4. Find p.
In the second position x = 12. p is known. find y.
2y will give you the required result.

 

[unrealmatt3]

hey thank rl.bhat for the welcome.
so i think i got it... first 16=4*P(x) where x=2 therefor P = 2
2nd y^2=4(2)(12)
Y^2 = 96
y=4 $$\sqrt{6}$$
then 2y = 19.6 meters

 

[rl.bhat]

That is right.