document.write( "Question 1658: how do you solve this quadratic equation.y >/= x^2-3x+1 \n" ); document.write( "

Algebra.Com's Answer #543 by AnlytcPhil(1810) $\"\"$ $\"About$

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\n" ); document.write( "How do you graph the solution set for this quadratic inequality?:
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\n" ); document.write( "y > x² - 3x + 1
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\n" ); document.write( "You first graph the equation of the boundary equation, which is
\n" ); document.write( "found by replacing the inequality \" > \" by an equal sign
\n" ); document.write( "\" = \": Since the inequality is \" > \" rather than \" > \" we draw
\n" ); document.write( "the graph with a solid line.
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\n" ); document.write( "[When the inequality sign is \" > \" or \" < \",
\n" ); document.write( "we draw the graph solid since it includes the boundary line,
\n" ); document.write( "and when the inequality is \" > \" or \" < \" we draw it dashed or
\n" ); document.write( "dotted].
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\n" ); document.write( "So we wish to graph the boundary y = x² - 3x + 1
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\n" ); document.write( "Make a table of points:
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\n" ); document.write( "` x | y ` `|` `point` `|
\n" ); document.write( "` ----------------------
\n" ); document.write( "`-1 | 5 ` `|` (-1,5) ` |
\n" ); document.write( "` 0 | 1 ` `|` `(0,1) ` |
\n" ); document.write( "` 1 |-1 ` `|``(1,-1)` `|
\n" ); document.write( "1.5 |-1.25 |(1.5,-1.25)|
\n" ); document.write( "` 2 |-1 ` `|` (2,-1)` `|
\n" ); document.write( "` 3 |`1 ` `|` `(3,1)` `|
\n" ); document.write( "` 4 |`5 ` `|` `(4,5)` `|
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\n" ); document.write( "Plot these points and you get this graph
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\n" ); document.write( " $\"graph%28200%2C200%2C-2%2C5%2C-3%2C12%2Cx%5E2-3x%2B1%29\"$
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\n" ); document.write( "Now the rules for shading, which I can't do here, but which
\n" ); document.write( "you can do on your paper are:
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\n" ); document.write( "If the inequality is \" > \" or \" > \", then shade the area
\n" ); document.write( "ABOVE the boundary graph.
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\n" ); document.write( "If the inequality is \" < \" or \" < \" then shade the area
\n" ); document.write( "BELOW the boundary graph.
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\n" ); document.write( "So since the inequality is \" > \" you are to shade the area
\n" ); document.write( "ABOVE (inside) the boundary graph drawn above.
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\n" ); document.write( "Edwin J \n" ); document.write( "

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