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To generalize then, solving for the two terms,
p , it is necessary to
consider a set of observations that apply to the solutions of all quadratic equa-
tions. These observations are as follows:
p and
If the value of a is greater than zero, then there are two solutions (
p ).
n
If the value of a equals zero, then only one solution is correct.
n
If the value of a is less than zero, no solution exists. (You cannot in this
situation find the square root of a negative number.)
n
Quadratic Appearances
You can draw on the discussion that previous chapters provided to explore a few
basic ideas that apply to representing quadratic equations. Consider, for exam-
ple, that quadratic equations possess a degree of 2. A variable with an exponent of
2 represents a square. When you graph values you generate using a square, the
values you generate are positive. For this reason, in the functional form of a
quadratic equation, the values of a domain ( x ) generate positive values of a
range ( y ). The resulting geometrical representation for this graph is a parabola.
Figure 9.1 illustrates a parabola generated by the equation y ΒΌ x 2 .
Figure 9.1
A rudimentary quadratic function generates a parabola.
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