What happens if we change “k” in y = a | x - h | + k?

The parameter “k” translates (moves) the graph horizontally.

• If “k” is positive (k > 0), then the absolute value graph moves up.
• If “k” is negative (k < 0), the absolute value graph moves down.

Example

Describe the effect on the graph of y = 2 | x - 4 | + 5 if the equation is changed to y = 2 | x - 4 | - 2 ?

Comparing the two equations, they differ only by the last constant, which is “k”.

• Remember that “k” ONLY affects vertical movement of the graph.
• In the first equation y = -7 | x - 8 | + 5 ⇒ k = 5

This is the parent graph translated nine units up, since k = 5 and 5 > 0.

• In the second equation y = 2 | x - 4 | - 2 ⇒ k = -2

This is the parent graph translated two units down, since k = -2 and -2 < 0.

Changing from k = 5 to k = -2, shifts the graph 7 units down.

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