Ahiker walks up and down a hill. the hill’s cross section can be modeled by the function y = – 3/4|x – 300| + 400 where x and y are measured in feet and d: [0, 600]. how far does the hiker walk?

Find the vertex by either graphing ( See attached picture) or setting the value in the absolute value bracket to 0:

Vertex is (300,400)

Because it is symmetrical, find the length of one side and double ot for total distance.

Using the distance formula shown on the attached picture.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.