Question

Draw the graph for $y=|x^2-2x-3|$

Answer 1

As we know the graph for $y=x^2-2x-3=(x-3)(x+1)$ is a parabola;
So to sketch $y=|x^2-2x-3|$ we have to follow two steps:
$\left(i\right)$Leave the positive part of $y=x^2-2x-3$, as it is
$\left(ii\right)$Take the image of negative part of $y=x^2-2x-3$,
i.e., the part below $x-$axis in the $x-$axis as plane mirror shown below.
Graph for $y=x^2-2x-3=(x-3)(x+1)$ is plotted as

x	-2	-1	0	1	2	-3	3	$-\infty$	$\infty$
y	5	0	-3	-4	-3	12	0	$\infty$	$\infty$