How is the graph of y = |x² - 12x + 20| related to the graphs of y = x² - 12x + 20 and y = -(x² - 12x + 20)? Explain your answer briefly.
The graph of y = |x² - 12x + 20| is
- the same as the graph of y = x² - 12x + 20 for x ≤ 2 or x ≥ 10, and
- the same as the graph of y = -(x² - 12x + 20) for 2 < x < 10.
This is because
- when x ≤ 2 or x ≥ 10, x² - 12x + 20 is non-negative, so |x² - 12x + 20| = x² - 12x + 20, and
- when 2 < x < 10, x² - 12x + 20 is negative, so |x² - 12x + 20| = -(x² - 12x + 20).