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The
Quadratic Formula:
I cannot apply the Quadratic Formula yet! The Formula only applies once I have "(quadratic) = 0", and I don't have that yet here. The first thing I have to do is move the 1 over, so I'll have "= 0" on the righthand side: Copyright © Elizabeth Stapel 20002011 All Rights Reserved x^{2} + 2x – 1 = 0 Letting a = 1, b = 2, and c = –1, the Quadratic Formula gives me: Then the answer is x = –2.41, x = 0.41, rounded to two decimal places.
The xintercepts (that is, the solutions from above) are marked in red. This relationship between the value inside the square root (the discriminant), the type of solutions (two different solutions, one repeated solution, or no real solutions), and the number of xintercepts (on the corresponding graph) of the quadratic is summarized in this table:
Probably the most important thing to remember when using the Quadratic Formula (other than the Formula itself, which you should memorize) is that you must do each step clearly and completely, so you don't lose your denominators or plusminuses or square roots. Don't skip stuff, and you should do fine. Warning:
If you get in the habit of "forgetting" the square root sign
until the end when the back of the book "reminds" you that you
"meant" to put it in, I'll bet good money that you'll mess up
on your test. If you get in the habit of "forgetting" the plus/minus
sign until the answer in the back "reminds" you that it belongs
in there, then you will almost certainly miss every single problem where
the answer doesn't have a square root symbol in it to "remind"
you to put the plus/minus sign back in. That is, any time your answer
is supposed to be something like "x
= 5 ± 10", you
will put down "x
= 5 + 10 = 15",
and will have no idea how the book (or test) got the second answer of
"x
= –5". If you
get sloppy with the denominator "2a",
either by forgetting the "a"
or by not dividing the entire numerator by this value, you will
consistenly get the wrong answers. I've been grading homework and tests for too many years to be kidding about this. Really, truly; you want to do your work neatly and completely every single time! << Previous Top  1  2  3  Return to Index



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