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

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

• If “h” is positive (h > 0), the absolute value graph moves to the right.
• If “h” is negative (h < 0), the absolute value graph moves to the left.

Example

Describe the effect on the graph of y = | x - 1 | if the equation is changed to y = | x + 8 |?

If y = | x - 1 | ⇒ h = 1

• This is the parent graph translated one unit to the right, since h = 1 and 1 > 0.

If y = | x + 8 | = | x – - 8 | ⇒ h = - 8

• This is the parent graph translated eight units to the left, since h = -8 and -8 < 0.

Changing from h = 1 to h = -8 shifts the graph 9 units to the left.

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