tag:blogger.com,1999:blog-8537494321067959493.post7330360555399167467..comments2024-03-04T21:07:02.238-08:00Comments on BorschtWithAnna: Axis of symmetry for a quadratic functionAnna Blinsteinhttp://www.blogger.com/profile/13960574914938362477noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8537494321067959493.post-71725535600781718842014-02-24T09:49:06.695-08:002014-02-24T09:49:06.695-08:00Definitely - I've done it both ways. With stud...Definitely - I've done it both ways. With students that can abstract it, factoring x out of ax^2 + bx and then using the zero product property totally makes sense. For students that aren't ready for that leap of abstraction, they can usually still "see" the pattern as long as there are numbers in place of the a and b in the equation.Anna Blinsteinhttps://www.blogger.com/profile/13960574914938362477noreply@blogger.comtag:blogger.com,1999:blog-8537494321067959493.post-76394497929803161132014-02-24T09:47:09.981-08:002014-02-24T09:47:09.981-08:00Thanks! That's a great point. I definitely emp...Thanks! That's a great point. I definitely emphasize the axis of symmetry equation "hidden" inside the quadratic formula, but I like the idea of writing it as two separate functions for greater emphasis.Anna Blinsteinhttps://www.blogger.com/profile/13960574914938362477noreply@blogger.comtag:blogger.com,1999:blog-8537494321067959493.post-70142824244649547062014-02-23T21:34:04.935-08:002014-02-23T21:34:04.935-08:00I like your idea. I think that I would have kids f...I like your idea. I think that I would have kids factor the quadratic y=ax^2+bx to y=x(ax+b) and find the zeros x=0 and x=-b/a and then say the axis of symmetry is halfway between the two zeros... Maybe... I guess it would depend on the level of the students.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8537494321067959493.post-41718420608700591622013-12-10T10:22:02.504-08:002013-12-10T10:22:02.504-08:00Anna
Thanks for sharing your work and story. Along...Anna<br />Thanks for sharing your work and story. Along these lines - I was at a workshop at Exeter in the summer a few years back. A quadratic presentation urged us to be careful whenever we write the quadratic formula. Rather than write one big fraction, break it up as (-b/(2a)) +/- blah blah blah<br />This clearly draws your eyes to the axis of symmetry piece of the solution. It re-emphasizes the symmetric relationship between the roots and helps reinforce the fact (later on) that complex roots come in conjugate pairs.<br />Just another think to think about Anonymousnoreply@blogger.com