The Quadratic Formula

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The Quadratic Formula
By Emily Parish MGF 1107
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Yes, it does look pretty scary, but I will prove
to you that it really isnt. Youll find its
only a matter of plugging in numbers.
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The Quadratic Formula is derived from the
quadratic equation ax2bxc0. For history
on the quadratic equation view the URL
below. http//www-groups.dcs.st-andrews.ac.uk/his
tory/HistTopics/Quadratic_etc_equations.html So
how do we get from this equation to the
Quadratic Formula?
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View the following website for a detailed
explanation of how the equation ax2bxc0 algeb
raically evolves into the Quadratic
Formula. http//www.sosmath.com/algebra/quadratice
q/quadraformula/quadraformula.html Continue on to
the next slide for an animated explanation.
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Before we try the formula, there are a few things
that you will want to keep in mind while using it.
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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 gt0. 2. You can
have 1 real root if the discriminate 0. 3. But
you can have NO real roots if the discriminate is
lt0.
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• 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.

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Now lets try one. . .
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Well start with the equation x23x-40. Yes,
this equation can be factored out to
(x4)(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 x23x-40 to the quadratic equation,
ax2bxc0.
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In comparing the two equations we see that a1,
b3, and c-4. Now all we have to do is plug this
into the Quadratic Formula.
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After you plug the numbers in you simply solve
the equation.
Dont forget that the means you have to try the
and the giving you two answers. In this
case, x-4, 1.
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See that wasnt 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/quadf
orm.html http//coolmath.com/calculators/quadratic
.htm Pretty neat, huh? ?
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Now lets try one that looks a little more
complicated (without plugging the numbers into
the website I just gave you).
But this time youre on your own!!
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48x264x-350 First of all decide what a, b, and
c equal, and remember its only a matter of
plugging in numbers! You can do it!
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Did you get x5/12, -7/4 ? That should be your
answer. If you dont understand how this is
correct, check this website http//www.csun.edu/m
ath095/schedule/notes/mod8/quadratic/quadraticform
ula.html1. But if you did get it right, hurray!
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See, the Quadratic Formula isnt as scary as it
seems!
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References http//coolmath.com/calculators/quadrat
ic.htm http//www-groups.dcs.st-andrews.ac.uk/hi
story/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 ht
tp//www.sosmath.com/algebra/quadraticeq/quadrafor
mula/quadraformula.html http//www.csun.edu/math
095/schedule/notes/mod8/quadratic/quadraticformula
.html1