Question

Graph this equation Y = IxI – 3 ...?

Answer 1

this will be your typical absolute value graph (it looks like a "v"), just moved three units downwards. the vertex will be at (0, -3). the x-intercepts will be at (-3, 0) and (3, 0). i attached an image in case you can't visualize it!!

but, to graph it by hand: find your x-intercepts by plugging in a 0 for y.

0 = |x| - 3
add 3 to both sides
|x| = 3

then because it's absolute value you set it to both pos and neg three:
x = 3
and
x = -3

those are your x-intercepts and because it's just a downward shift, it's a pretty standard graph. you don't really need to plug in points, but you can always do an input/output table if ya feel so inclined

Answer 2

We substitute x = 0 to obtain the y intercept, that is:
(0 , -3)
Next, the x intercepts are found by equating y to 0:
3 = |x|
x = 3, x = -3;
(3 , 0) and (-3 , 0) are the x intercepts

Finally, we join the x-intercepts to the y-intercepts using straight lines and the graph is formed. It is in the shape of a "V", characteristic of this type of function.