Question

A tunnel on a bike trail is being designed similar to the picture below. The height of the new bike tunnel, y, in feet, is given by the following equation, where x is the horizontal distance, in feet, from the center line of the opening of the tunnel. Note that negative x-values indicate the distance to the left of the center line, and positive x-values indicate the distance to the right of the center line. Plot the points on the graph where the height of the tunnel is a maximum and where the height of the tunnel is zero feet.

Answer 1

Explanation:

Answer 2

we have that

`y=-x^2+36`

we know that

Is the equation of a vertical parabola open down

so

the vertex is a maximum

step 1

convert the equation of the parabola in the vertex form

`y=-x^2+36`

`y-36=-x^2`

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0

so

for y=0

`-x^2+36=0`

`x^2=36`

`x=(+/-)6`

the points are (-6,0) and (6,0)

see the attached figure