A tunnel goes through a mountain whose shape can be modeled

Question

A tunnel goes through a mountain whose
shape can be modeled by
h = −63x
2 + 17x
where h is the height (in miles) and x is the
distance (in miles) from the opening of the
tunnel.
Find the length of the tunnel.
Answer in units of miles.

Answer 1

h = -63x^2 +17x

where x = distance from the opening of the tunnel and

h = height of the tunnel

height = 0 at both ends of the tunnel

h=0 = -63x^2 +17x = x(-63x +17)

-63x +17 = 0

x = 17/63 = length of the tunnel = about 0.2698 miles

= about a quarter mile