Question

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.

Answer 1

The basic formula of a parabola is;

y -k= 4a (x-h)^2

Solving for this, the vertical clearance 7m forom the edge of the tunnel must be

15.7m

Hope this helps! Goodluck!

Answer 2

Vertex at the origin and opening down → y=ax^2
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4

y=ax^2→y=-(1/4)x^2

7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4

Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m

Please, see the attached file.

Answer: Third option 15.75 m