Time for investigation, almost 75 min[br]Earlier in the course: Enough playing around with the graphs of quadratic functions & formula for zeros [b][url=http://chart.googleapis.com/chart?cht=tx&chl=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D][img width=131,height=44]https://lh4.googleusercontent.com/GMPMB9Wgr8h-SKFQxIi8kp98-oxa-pYkDEzfoyFX2OOP7PvcCN9AnQvVRxXTGlDfXx6ampw_OoQ9uqEc2Sw_nypjmNv0DKpIbDsjrAkLx2mXSU8DXxmf1FQ7XSrCp2NJ6yBOspJg[/img][/url].[br][/b]Goal: Students find out which part of formula above influences the number of solutions of second order polynomial.[b][br][br][/b]This idea is simple, takes time for students to do and gives them opportunity to rehearse how to solve zeroes, how to express themselves mathematically.[b][br][br][/b]Students are asked to do following ( in small groups)[b][br][/b][list=1][*]With Geogebra, find out second order polynomial, which has a) 2 b) 1 c) 0 zeros.[/*][*]By hand, calculate the zeros and find out, which part of the formula influences the number of solutions.[/*][*]Make your own theory. ( Formulate your theory so that it uses same letters as in the formula for zeros of second order polynomial. Write down your theory, send or show to teacher.[/*][*]Use your theory, to find out for which k, equation [b][url=http://chart.googleapis.com/chart?cht=tx&chl=%28k%2B3%29x%5E2%2Bkx%2Bk-3%3D0][img width=184,height=19]https://lh4.googleusercontent.com/LTc11xxrT6PzQ_oM4HJnaNpAQTx-f5k65IbtG_Vz-KoT-AJrep0unDCZdeZZHsC0LvVh4FtnD-m5daFYWKf_-dK82CBz1QUS4THeGtwbfsbPfo6JV1ZjjYzBFvVDa8Wa53I7lN1a[/img][/url][/b] has 2 solutions, 1 solution or 0 solutions. You can use Geogebra to solve this. ( there are at least 2 possibilities to go, students use slider or CAS)[br][/*][/list]