tag:blogger.com,1999:blog-8231784566931768362.post2687430333510681203..comments2023-09-09T08:21:55.454-04:00Comments on MathNotations: Using "SAT-Type" Problems to Develop Understanding of Quadratic Functions in AlgebraDave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8231784566931768362.post-12287629494894662062009-08-03T06:31:19.265-04:002009-08-03T06:31:19.265-04:00Another thought, Pat...
A variant of the form you ...Another thought, Pat...<br />A variant of the form you suggested used to show up when studying the focus-directrix form of the parabola:<br />y-k = (1/4p)(x-h)^2.<br />I'm assuming this is still taught in most precalculus curricula. I can't imagine not discussing the significance of the focus of a parabola!Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-81283381034528969072009-08-02T07:21:53.930-04:002009-08-02T07:21:53.930-04:00tc and Pat==
Thanks for your support!
tc--
Yes, I...tc and Pat==<br />Thanks for your support!<br /><br />tc--<br />Yes, I wonder what they would do with that clever variation. If they grasp the symmetry, it's obvious, but...<br /><br />Pat--<br />I agree with you that texts and curriculum should be more consistent with translations, since the point-slope form of a line and the general "h-k" forms for other conics follow your suggestion. Then of course they wouldn't find it so strange or confusing. However, the emphasis in most curricula/texts is on the function aspect for linear and quadratics so the "y =' or "f(x) =" forms have won out for now. This is usually students' introduction to functions so it's believed that the "y = " form is important. Until of course someone writes a text using your approach! <br /><br />Now do either of you believe that some students would be test-savvy or clever enough to "plug in" a simple value for the parameter 't' and use a graphing calculator to solve this problem? Currently, testmakers believe a parameter discourages use of a calculator but I've seen otherwise!Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-40234800929947227702009-08-01T13:23:04.892-04:002009-08-01T13:23:04.892-04:00Dave,
Nice problem. I would like to get back and ...Dave,<br />Nice problem. I would like to get back and try it with my kids... I focus on the vertex form a lot and really push symmetry, so I hope they would do well, but will shut up before I jinx them... <br />I think part of the problem is that we almost never encourage students write stuff like y-3 [or f(x)-3]= 2(x-4). Many software programs (TI-8*) for example, won't allow entries of this kind. I think the idea of "centers" and shifts are more difficult when they see a different shift inside the parentheses vrs outside.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-83443826454531670862009-08-01T11:58:33.903-04:002009-08-01T11:58:33.903-04:00Nice one, Dave!
I guess the advanced students st...Nice one, Dave! <br /><br />I guess the advanced students start thinking more in terms of detailed solutions rather than looking at the basic aspects (or rather, big picture) like symmetry.<br /><br />For the non-SAT advanced student, I would make it more interesting by saying f(-7.3)=f(a) where a>0, and see what they come up with. <br /><br />TCUnknownhttps://www.blogger.com/profile/06449079338919787252noreply@blogger.com