y = |x| is an absolute value function with vertex at (0, 0).
In a function, if you replace x with x - h, the graph shifts h units horizontally.
If you replace y with y - k, the graph shifts k units vertically.
Move the 7 to the left side.
y = |x - 4| - 7
y + 7 = |x - 4|
Now compare this function with the parent function y = |x|.
x has been replaced with x - 4. h = 4. The horizontal shift is 4 units to the right since 4 is positive.
y has been replaced with y + 7. We need to write y + 7 as y - k, so we write y - (-7). Then we see that k = -7. The vertical shift is 7 units down since 7 is negative.
Answer: the vertex is (4, -7), choice B.
