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Topic: Algebra Regents
Replies: 10   Last Post: Jun 21, 2012 5:56 AM

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Nick B

Posts: 96
Registered: 9/23/07
Re: Algebra Regents
Posted: Jun 21, 2012 5:56 AM
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x- and y-intercepts are points. See below from Wolfram MathWorld, which is a formalized online math encyclopedia that is widely used by the mathematical community:

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 non-real 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 x-intercepts. 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 x-intercepts for a ninth grader. Of all misconceptions a ninth grader could have, the distinction between roots and x-intercepts seems to me to be one of the most pedantic, especially considering that, for ninth graders, there is a 1-to-1 correspondence between roots and x-intercepts. 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.

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