Answer:
1) A "U" shape or curve
2) a "V" or each arm straight out and point diagonally upward.
A quadratic graph involves a single variable with the highest degree being 2, such as x^2, x^2 + 4x + 2, etc. The graphs all have a U type shape, it may be opening down or up, but it will always be a U type shape.
An absolute value graph involves an equation such as y = |x| + 2, y = |x|, or y = |x - 2|, these all have a v shape. You may not include a quadratic term with the absolute value graph, otherwise it changes the shape slightly (the "arms" are curved)
Honestly you can potentially transform either graph into a different shape. For example y = .00000001x^2, while quadratic, is VERY close in shape to a line.
Of course if we maximize the graph and look at a point such as x = 10^10, we will find a great value for y and see that it does indeed curve, it just takes VERY large values of x.
