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Notes for 1.4 Quadratic Equations (pp. 119 – 123)
Topics: Solving Quadratic Equations by Zero-Factor Property,
Square Root Property, and Quadratic Formula; Solving for a
Variable; Discriminant; Restrictions and Domain
The definition of a quadratic equation is an equation that can be written as _________________,
where a, b, and c are ___________________ and _____________. A quadratic equation that is
written in the form 20ax bx c++= is in _____________________________. The degree of a
quadratic equation is _____.
I. Solving a Quadratic Equation using the Zero-Product Property (p. 166)
The Zero-Product Property states that if ab = 0, then ________or _________ or both. This
means that each factor can be set to = 0. This method should be used when the equation can be
easily factored.
Ex. 2
23xx−=
(All quadratics must = 0 before factoring)
Now split into 2 independent parts and solve separately.
II. Solving a Quadratic Equation using the Square Root Property (p. 117)
This property allows us to use a _________________ to undo a single square term or a
parentheses that has been squared. We always get 2 answers, the _________ and the
__________ of the radical. This method should be used only when the quadratic has a single
square term.
Ex. 220a= (Note that the number is positive)
220a=± (This number under the radical, 20, has a perfect square factor that can be
used to help simplify this radical.)
a = 45±i
a = 25±
Ex. 249b=− (This cannot be done in the real number system, since there are no twin factors
that can multiply and give us a negative anything, even a 49.) Our solution for this is
∅
(null
set), which means that it can’t be done. The text uses imaginary numbers here, which is not part
of our class content.
Ex. 2
(1)18y−=
Note: The “smart way” to factor 18 is as 9 * 2, not 6 * 3.
Ex. 25
(1)2
p−=
