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The Quadratic Formula

The Quadratic Formula. By Emily Parish MGF 1107. Yes, it does look pretty scary, but I will prove to you that it really isn’t. You’ll find it’s only a matter of plugging in numbers. The Quadratic Formula is derived from the quadratic equation: ax 2 +bx+c=0 .

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The Quadratic Formula

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  1. The Quadratic Formula By Emily Parish MGF 1107

  2. Yes, it does look pretty scary, but I will prove to you that it really isn’t. You’ll find it’s only a matter of plugging in numbers.

  3. The Quadratic Formula is derived from the quadratic equation: ax2+bx+c=0. For history on the quadratic equation view the URL below. http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Quadratic_etc_equations.html So how do we get from this equation to the Quadratic Formula?

  4. View the following website for a detailed explanation of how the equation ax2+bx+c=0 algebraically evolves into the Quadratic Formula. http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html Continue on to the next slide for an animated explanation.

  5. Before we try the formula, there are a few things that you will want to keep in mind while using it.

  6. Remember these three parts that concern the discriminate of the formula (which is the part under the square root). 1.You can have 2 different real roots if b2-4ac is >0. 2.You can have 1 real root if the discriminate =0. 3.But you can have NO real roots if the discriminate is <0.

  7. More to remember. . . • Know that if your quadratic equation is not equal to zero, the formula will NOT work. • Never forget the 2a denominator in your formula and that it is not under the square root only; it is under the entire equation to the right of the equal sign. • Remember to keep the ± in your problem until the end. • Remember b2 is the square of ALL of b, including the sign that follows it in the equation.

  8. Now let’s try one. . .

  9. We’ll start with the equation x2+3x-4=0. Yes, this equation can be factored out to (x+4)(x-1)=0, but frankly the Quadratic Formula is much more reliable because not all equations will factor. To begin solving the problem we must relate x2+3x-4=0 to the quadratic equation, ax2+bx+c=0.

  10. In comparing the two equations we see that a=1, b=3, and c=-4. Now all we have to do is plug this into the Quadratic Formula.

  11. After you plug the numbers in you simply solve the equation. Don’t forget that the ± means you have to try the + and the – giving you two answers. In this case, x=-4, 1.

  12. See that wasn’t complicated was it? The following websites have JavaScript programs that solve quadratic equations for you! Not that you would want to cheat or anything , but try plugging the numbers in from the equation that we just solved. http://mav.net/troy/quadform.htm http://school.discovery.com/homeworkhelp/webmath/quadform.html http://coolmath.com/calculators/quadratic.htm Pretty neat, huh? 

  13. Now let’s try one that looks a little more complicated (without plugging the numbers into the website I just gave you). But this time you’re on your own!!

  14. 48x2+64x-35=0 First of all decide what a, b, and c equal, and remember it’s only a matter of plugging in numbers! You can do it!

  15. Did you get x=5/12, -7/4 ? That should be your answer. If you don’t understand how this is correct, check this website http://www.csun.edu/~math095/schedule/notes/mod8/quadratic/quadraticformula.html#1. But if you did get it right, hurray!

  16. See, the Quadratic Formula isn’t as scary as it seems!

  17. References http://coolmath.com/calculators/quadratic.htm http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Quadratic_etc_equations.html http://mav.net/troy/quadform.htm http://school.discovery.com/homeworkhelp/webmath/quadform.html http://www.purplemath.com/modules/quadform.htm http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html http://www.csun.edu/~math095/schedule/notes/mod8/quadratic/quadraticformula.html#1

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