Grade 11 Precalculus

Question

A tunnel is in the shape of a parabola. The maximum height is 20 meters and it is 20 meters wide at the base. What is the vertical clearance 5 meters from the edge of the tunnel?

Answer 1

You must always start with a labelled diagram, like this one:

Now, use the standard quadratic function in the vertex form: f(x) = a(x - h)² + k

Plug in the vertex (10,20): f(x) = a(x - 10)² + 20

Plug in any other point on the graph to determine the value of "a". I'll use (0,0):

0 = a(0 - 10)² + 20

a = -0.2

f(x) = -0.2(x - 10)² + 20

Now you can plug in x = 5

f(5) = -0.2(5 - 10)² + 20 = 15