This, I found out is a radical way to graph quadratic equations! Actually, I discovered this on Youtube around 4 years ago and up to now, I found out that even Math teachers still did not know about this until we were on a topic on mentoring. I am telling you, most of the things I am teaching today were not taught in my college days! Things were bumped on as I progressed in my teaching career. It was around the end of the 2nd grading period this year that then I asked a co teacher on how he taught the topic Graphing of Quadratic functions and I was surprised that he said he used a table of values, or determining the vertex first and from there, getting symmetrical points/ or if there x intercepts. I taught him immediately the quick fix and trick to this even without that table of values, or other way/s around to. And he seemed to like it. That was my first instance of mentoring as a Master Teacher. The topic to beat is graphing quadratics. I thought to myself that it’s more likely that students will like this. Well, most of them anyway. For others are stubbornly closed to learning and more focused on being petiks. (slang for easy-go-lucky)
First, we need a quadratic to graph: How would you, for instance graph the quadratic function in the vertex form y= (x-2)2 + 3? First you need to identify the vertex . Very obviously, it’s at (2, 3) Then from the graph paper just considering the step pattern count 1, 3, 5, 7, … The count comes from the parent graph of y = x2. There are spaces of 1, 3, 5, … from the vertex to the 1st symmetrical point on the right, from there to the 2nd symmetrical point and so on. The count is over 1 up 1, over 1 up 3, over 1 up 5, and so on. For as long as the a part = 1 or -1 when the parabola opens upward or downward. So there. Enough fun topic to mentor my co teachers with because they themselves enjoyed the step pattern count which is with so much ease. And the graph count changes when a>1 . When the equation for instance is y = 2 (x+3)2 -4, then the count swerves from 1, 3, 5 to 2, 6, 10,… and when a= 3, as in y = 3(x-4)2 -1 , from
(4, -1) upward, the count becomes 3, 9, 15, … and the parabola gets narrower as a increases.
Inversely, when a is negative, then the parabola opens downward but the count is now, over 1 down 1, over 1 down 3 instead of up 1 and up 3. Multiply the count pattern by whatever is the apart . If graphing y = -2(x-1)2 +3, then the count shifts to over 1, down 2, over 1 down 6 and so on. If a= -3, then count begins by over 1 down 3, over 1 down 9 and so on. And so graphing seems just like a breeze just like in graphing linear functions where counting takes place likewise. This is more fun for Math students. Of course the presentation& the motivation to succeed on this and for them to enjoy depend on you: their Math teacher! There are many situations actually. Let us have another situation where the quadratic is in standard form. What do you do? That’s right! Determine the vertex and get it done in vertex form. We won’t go with the details of the formula. As a Math teacher, you ought to know it. If you have read this far, then you are one. Determine the vertex and count in the step pattern and voila, you would have conquered the graphing techniques in Quadratics.
By the way, thanks to my co teachers for the opportunity to mentor them. Not all are agreeable to such. Others may view mentoring as a blow to their pride. Honestly, I was amazed to have known this thing from Youtube channel. I was a slave of that table of values once, I admit. Now I know it’s for sissies! No more enthrallment of that kind from now on. It takes research for one to know and mentoring what you have learned to make it fruitful for your clientele – the community of learners who depend upon you!
By: Ronaldo V. Tiangco | MT I | MNHS Poblacion
