Question 350752
The two are similar as they both have vertical symmetry. In other words, if you divide the graph down the middle, one side is merely a reflection of the other. Also, they both have a vertex (either a highest or lowest point). Finally, both quadratic and absolute value equations can either have 0, 1, or 2 x-intercepts.



However, a quadratic plots a parabola (a bowl shaped curve) while an absolute value graph plots a "V" shaped graph (see below). Also, the vertices of each are different. The quadratic has a smooth vertex while an absolute value has a sharp vertex. Also, notice how the quadratic has faster growth than the absolute value.




Example of a quadratic



{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,(x-3)^2+2)

)}}}



Example of an absolute value

{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,abs(x-2)+1)

)}}}