The quadratic formula is an effective method for solving quadratic equations especially because it can identify all real solutions as well as complex solutions. That is, it is not limited to identifying rational solutions. The formula itself can look a little intimidating at first and it must be memorized if you are going to use with pencil and paper. By watching one of the music videos below you may find it easier to memorize, in fact maybe even hard to forget. There is more you will need to know about how to apply quadratic formula below the videos, but for now try get a handle on what the formula is.
or any of these
Now that you have seen the quadratic formula, it is time to learn how to put it to use.
You may be finding that using the quadratic formula over and over again is getting tedious. Thankfully we have computers and programs that are really repeating tedious tasks.
Using functional spreadsheet software like Excel, Google.Sheets, or the spreadsheets on your Ti-nSpire allows you to make tool where you input a, b, and c and it will calculate the value(s) of x (as long as they are real solutions. Below is the start of such a spread sheet, some of the formatting is laid out but none of the functions or program is made, that part is up to you. It takes a little while to get everything working properly but can save time in long run due to how long the quadratic formula takes by hand. Link to Sheet
The Quadratic Formula
The quadratic formula is an effective method for solving quadratic equations especially because it can identify all real solutions as well as complex solutions. That is, it is not limited to identifying rational solutions. The formula itself can look a little intimidating at first and it must be memorized if you are going to use with pencil and paper. By watching one of the music videos below you may find it easier to memorize, in fact maybe even hard to forget. There is more you will need to know about how to apply quadratic formula below the videos, but for now try get a handle on what the formula is.
or any of these
Now that you have seen the quadratic formula, it is time to learn how to put it to use.
Skills Practice:
You may be finding that using the quadratic formula over and over again is getting tedious. Thankfully we have computers and programs that are really repeating tedious tasks.
Using functional spreadsheet software like Excel, Google.Sheets, or the spreadsheets on your Ti-nSpire allows you to make tool where you input a, b, and c and it will calculate the value(s) of x (as long as they are real solutions. Below is the start of such a spread sheet, some of the formatting is laid out but none of the functions or program is made, that part is up to you. It takes a little while to get everything working properly but can save time in long run due to how long the quadratic formula takes by hand.
Link to Sheet
Extension:
Visit the Oswego City School District Regents Exam Prep Center's website and learn how the discriminant can tell you about the number of roots you should expect to have in a given number system. This uses information about the graph of a quadratic function so it may help to view Understanding the Graph first.