Nick B
Posts:
77
Registered:
9/23/07


Re: #34 Algebra Regents
Posted:
Jun 21, 2012 3:39 AM


x and yintercepts are points. See below from Wolfram MathWorld, which is a formalized online math encyclopedia that is widely used by the mathematical community:
http://mathworld.wolfram.com/yIntercept.html
Roots are solutions to an equation, which are not points but rather values. One way to think about the distinction here is to consider equations for which nonreal roots exist (e.g., the roots of f(x) = x^2 + 4). The roots are x = 2i and x = 2i but the graph of f(x) = x^2 + 4 lacks xintercepts. Hence, the representation of roots as points is not possible.
I think what could be discussed is the actual conceptual significance between the roots and the xintercepts for a ninth grader. Of all misconceptions a ninth grader could have, the distinction between roots and xintercepts seems to me to be one of the most pedantic, especially considering that, for ninth graders, there is a 1to1 correspondence between roots and xintercepts. My personal scores were not greatly affected by this, but in talking to colleagues in many schools, many students lost 100's based on losing a point for stating the roots as points. Has a student who listed the roots as values and not points shown that he or she has mastered a concept more than a child who reads too much into the directions "Using the graph..."? I think that is a tougher pill to swallow than the realization that, technically, roots are not points.

