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Factoring to Solve Quadratic Equations |
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This lesson will review the process of factoring as a method of
solving quadratic equations.
Def n:
Quadratic equations are any equations that contain a power of two
as the highest power in the equation. They are normally expressed
as  , where
a does not equal zero.
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Tidbit of info:
“Doesn’t QUAD
mean four???”
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Although in Latin the prefix "quadri" means four, the word "quadrus"
means a square (because it has four sides) and "quadratus" means
"squared." Consider other words such as: "quadrille,"
meaning a square dance; "quadrature," meaning constructing a
square of a certain area.
Quadratic equations were originally used in connection with
geometric problems involving squares. Since the second
power is called a "square," equations with the highest power
being two are called quadratic equations. |
Many of the simpler quadratic equations with rational
roots can be solved
by factoring.
| 1. |
Start with the equation in the form
(be sure it is set equal to zero!) |
| 2. |
Factor the left hand side
(assuming zero is on the right) |
| 3. |
Set each factor equal to zero |
| 4. |
Solve to determine the roots (the values
of x) |
Let's examine some possible situations:
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Factoring with GCF
(greatest common factor) |
Factoring with DOTS
(difference of two squares) |
Factoring Trinomials |
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Find the largest value that can be
factored from each of the elements of the expression.
Notice how the answers (the roots) can also be
observed as the locations where the graph crosses the x-axis. |
Look carefully at this example to refresh
this process: |
If you need more review on factoring, see
Math A Factoring.
Notice how the answers (the roots) can also be
observed as the locations where the graph crosses the
x-axis.
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Or
Isolate the Variable |
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Factoring Harder Trinomials |
Tricky
One!! |
Using Your
Graphing Calculator |
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If the leading coefficient is not equal to
1, you must think more carefully about how to set up your
factors.
If you need more review on factoring, see
Math A Factoring.
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Be sure to get the equation set equal to
zero before you factor.
Graph 2x2
- 5x + 2  |
The graphing calculator can be a very
helpful tool in solving quadratic equations and
checking factors.
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How to use
your
TI-83+ graphing calculator with
quadratic equations.
Click calculator. |
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