Answer:
The vertex of the graph of f(x) = |x - 13| + 11 is (13, 11).
Step-by-step explanation:
There is something called absolute value in the given function. It means two equations will result from it.
When [tex](x -13) > 0[/tex] the resultant equation is
[tex]y = f(x) = x - 13 + 11 = x - 2[/tex] - This will be the first equation
or
When [tex](x - 13) < 0[/tex] the resultant equation is
[tex]y = f(x) = -(x - 13) + 11 = -x + 24[/tex] - This will be the second equation.
The intersection of these lines will give the vertex as found by solving both equations at the same time.
[tex]y = x - 2[/tex]
[tex]y = -x + 24[/tex]
_________
[tex]2y = 0 + 22[/tex]
[tex]y = \frac{22}{2} = 11[/tex]
Replacing the value of [tex]y[/tex] for any one;
[tex]x = 11 + 2 = 13[/tex] (first one)
[tex]x = 24 - 11 = 13[/tex] (second one)
The vertex is (13, 11)
