SOLUTION: How do you find the x intercepts and y intercepts of the absolute Value y=|x-2|-4

Question 1139538: How do you find the x intercepts and y intercepts of the absolute Value y=|x-2|-4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

To find the y intercept, plug in x = 0 and simplify

Replace every x with 0. From here we use the order of operations PEMDAS.

The y intercept is -2. This means the graph crosses the y axis at -2 on the vertical number line. This is the location (0,-2). See the graph below.

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To find the x intercept(s), we replace y with 0 and solve for x.

Add 4 to both sides

or see note below

or Add 2 to both sides for each equation

or

The x intercepts are 6 and -2. In other words, the two x intercepts are at the locations (6,0) and (-2,0). These locations are where the graph crosses or touches the horizontal x axis. See the graph below.

note: I used the rule that if then or where k is some positive number. For example, if k is replaced with 7 then turns into or . This is because these two values (7 and -7) are both seven units away from the value 0 on the number line.

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Answers:
y intercept is -2
x intercepts are 6 and -2

Graph:

This V shaped graph is effectively two linear pieces "glued" together. The vertex is located at (2,-4). The graph was created with GeoGebra (free graphing software).

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