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Modulus Function

Construct the...

Question

Construct the graphs of the following functions.
$y = x^{2} - 2 | x | + 1 - 1.$

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Solution

Given equation is
$x^{2} - 2 | x | + 1 - 1 = x^{2} - 2 | x |$
There are $2$ cases
If $x > 0, x^{2} - 2 | x | = x^{2} - 2 x$
If $x < 0, x^{2} - 2 | x | = x^{2} + 2 x$
Thus, the two equations are $x^{2} - 2 x$ and $x^{2} + 2 x$
The graph is shown by the figure.

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