| Solving Quadratics |
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JUST THE FACTS:
When solving quadratic equations in one variable, ALWAYS START with the equation in STANDARD FORM by setting the equation equal to zero, i.e.
ax2 + bx + c = 0
For example...
x2 = 5x - 6 would become...
x2 - 5x + 6 = 0
| "Square Rooting" |
If there is no middle term (b=0), this is a very efficient method. Example x2 - 9 = 0 Just add 9 to both sides and take the square root of both sides... x = ± 3 Caution, if x2 is set equal to ANY negative number, there is no REAL solution, because there is no square root of a negative number. |
| Graphing |
Graphing is useful if you just need an approximate answer. You should recognize the impact of the leading coefficient (positive opens up, negative opens down; large coefficient is "skinny", fractional coefficient is "wide")
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| Factoring | 1) Always use when c = 0; i.e.
4x2 - 14x = 0 becomes 4x(x - 14/4) = 0 Solutions x = 0, 14/4 2) If you have a quadratic trinomial (a, b, & c are all non-zero), try to factor before using one of the next two methods.
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Completing the Square |
CTS can always be used, however is BEST SUITED for quadratics with a leading coefficient of 1 and with "b" an even number. x2 - 6x - 3 = 0 use CTS 3x2 - 6x + 4 = 0 use QF
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| Quadratic Formula (QF) |
"FAILSAFE"; The "QUADRANATOR" Always Works!
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