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

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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) About Me  (Show Source):
You can put this solution on YOUR website!

To find the y intercept, plug in x = 0 and simplify
y+=+abs%28x-2%29+-+4

y+=+abs%280-2%29+-+4 Replace every x with 0. From here we use the order of operations PEMDAS.

y+=+abs%28-2%29+-+4

y+=+2+-+4

y+=+-2

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.

y+=+abs%28x-2%29+-+4

0+=+abs%28x-2%29+-+4

0%2B4+=+abs%28x-2%29+-+4%2B4 Add 4 to both sides

4+=+abs%28x-2%29

abs%28x-2%29+=+4

x-2+=+4 or x-2+=+-4 see note below

x-2%2B2+=+4%2B2 or x-2%2B2+=+-4%2B2 Add 2 to both sides for each equation

x+=+6 or x+=+-2

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 abs%28x%29+=+k then x+=+k or x+=+-k where k is some positive number. For example, if k is replaced with 7 then abs%28x%29+=+7 turns into x+=+7 or x+=+-7. 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).