How to Find The Quadratic Equation From a Table/Points

So, those fun problems where you're given a table and asked, "Write the quadratic equation that represents the table/points shown?" That's what this video is all about.
Let me know if you have any questions or comments below. Thanks for watching!
Need a Math tutor?
www.toptiermath.com

[@davidcherepanov3953]

Very helpful as always! The video was a bit long but absolutely worth it. Great and detailed explanation, thank you very much

[@TopTierMath]

Yeah, it was a bit longer than I would have liked (working on that) but I'm glad it helped!

[@paules0099]

To find a, just divide the 2nd difference, which is 4, by 2. It always works! Less solving! Solve for b by substituting a, x, y, and c!

[@TopTierMath]

Absolutely! I teach the longer way initially because it also helps you practice solving systems of linear equations, which you’ll need in a typical Algebra 1 course and is taught before this topic. Once a student has that down, I’ll show them that trick as it’s definitely a time saver! I like to jokingly tell students “Remember this technique when you get to calculus and you’ll see why it works!” 😄

[@paules0099]

​@TopTierMath I get it. I had to learn algebra, geometry, and trigonometry because I wanted to be an engineer when I was in HS and college. Now, my daughter wants to be an artist and has zero interest in math. So, to get her through HS, I have "cheat sheets" and short cuts for her to memorize so she can pass it and get through it and graduate HS! Know what I mean?

[@justinm412]

@@paules0099 I initially majored in engineering, very cool! And yes, I definitely know what you mean. If you haven’t already, I would definitely recommend peppering in some SAT/ACT (whichever she will take) math questions so she gets the chance to think outside the standard “here’s your formula -> plug and chug” (more or less) and get exposed to the types of questions those exams ask. Theres a lot of free/paid SAT/ACT prep questions with whatever difficulty you’d like to work on so I would always recommend my students to practice them.

[@paules0099]

@@justinm412 If you only knew my daughter, LoL. She is easily confused by numbers! Especially irrational numbers and radicals! Math was a serious issue since 1st grade! She passes math by short cuts. She has zero interest when it comes to numbers. And, quite frankly, when I worked in engineering, all that math I learned, went out the window went solving real world challenges I faced in the work force, know what I mean?

[@tanman1000]

Thank you! Ps: here’s another trick. The change of change in y (4 in your case) divided by 2 is always a.

[@TopTierMath]

Absolutely! My students generally don’t see that from their teachers, but as they get experience I like to show them that trick. Definitely a time saver!

[@susanthomas4279]

We can make it even simpler by finding 'a' which is just dividing second difference by 2......ie, here, 4/2=2... Then use a point to get the value of 'c'

[@justinm412]

I love that method as well! My students generally aren't taught that way, but I show them that trick for future use ;)

[@chloesdeadinside8982]

what if the change of the change is not constant what do you do then?

[@TopTierMath]

Great question! If you're asked to find a quadratic equation from a list/table of points, the change in the change will always be constant. Do you have a particular example that you'd like for me to do a video on?

[@chloesdeadinside8982]

@@TopTierMath Yes thank you so much! I have a table and the question is "Find the quadratic function that is the best fit for​ f(x) defined by the table" The X's are 0,2,4,6,8, &10 and the Y's are 0,397,1596,3601,6403, &9990. Thank you so much for responding I've been stuck on this.

[@TopTierMath]

@@chloesdeadinside8982 my apologies for the late response. Are you being asked to do this by hand or are you allowed to use a graphing calculator?

[@aayaanfarooq9427]

@@TopTierMath i think it might’ve been a too late response 😅😅

[@clarckcharles5148]

Thanks

[@TopTierMath]

You're very welcome!