Question 1139538
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To find the y intercept, plug in x = 0 and simplify
{{{y = abs(x-2) - 4}}}


{{{y = abs(0-2) - 4}}} Replace every x with 0. From here we use the order of operations PEMDAS.


{{{y = abs(-2) - 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(x-2) - 4}}}


{{{0 = abs(x-2) - 4}}}


{{{0+4 = abs(x-2) - 4+4}}} Add 4 to both sides


{{{4 = abs(x-2)}}}


{{{abs(x-2) = 4}}}


{{{x-2 = 4}}} or {{{x-2 = -4}}} see note below


{{{x-2+2 = 4+2}}} or {{{x-2+2 = -4+2}}} 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(x) = k}}} then {{{x = k}}} or {{{x = -k}}} where k is some positive number. For example, if k is replaced with 7 then {{{abs(x) = 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: 
<font color=red size=4>y intercept is -2</font>
<font color=red size=4>x intercepts are 6 and -2</font>


Graph:
<img src = "https://i.imgur.com/rugTLI8.png">
This V shaped graph is effectively two linear pieces "glued" together. The vertex is located at (2,-4). The graph was created with <a href = "https://www.geogebra.org/">GeoGebra</a> (free graphing software).
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