What is the vertex of the graph of f(x) = |x - 13| + 11?
(- 11, 13), (- 13, 11), (11, 13), (13, 11)

Solution:

Because of the absolute value in the given function, two equations will result from it as shown below.

Case1:

When (x -13) > 0 the resultant equation is

y = f(x) = x - 13 + 11 = x - 2 --- (1)

Case2:

When (x - 13) < 0 the resultant equation is

y = f(x) = -(x - 13) + 11 = -x + 24 --- (2)

The intersection of these lines will give the vertex as obtained by solving equations (1) and (2) simultaneously. 

y = x - 2
y = -x + 24
_________
2y = 0 + 22

y = 22/2 = 11

Substituting the value of y in either (1) or (2) we get

x = 11 + 2 = 13 (using equation (1))

x = 24 - 11 = 13 (using equation (2))

The vertex is (13, 11)

What is the vertex of the graph of f(x) = |x - 13| + 11?

Summary:

The vertex of the graph of f(x) = |x - 13| + 11 is (13, 11).