Which of the following is the graph of $f (x) = | x^{2} - 4 |$ ?

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Solution

The correct option is A
Given that $f (x) = | x^{2} - 4 |$
Lets draw the graph of $y = x^{2} - 4$ .

Put $x^{2} - 4 = 0$
$\Rightarrow (x + 2) (x - 2) = 0$
The roots are $- 2, 2$ .
We will get the graph of $y = x^{2} - 4$ as:
Since we are asked to draw the graph of $y = | x^{2} - 4 |$ ,
the negative values of the ys will get flipped to the positive values of the y.
Therefore, we get:

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