document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157414>Question 1157414</A>: <I><SPAN STYLE=\"word-break: break-all;\">  f(x)=-3x^2+3x-2<BR>\n" );
document.write( "a. opens up or opens down<BR>\n" );
document.write( "b. vertex =<BR>\n" );
document.write( "c  axis of symmetry<BR>\n" );
document.write( "d. show algebraically how you know the function has no x-intercepts<BR>\n" );
document.write( "e internal where it is increasing and decreasing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780282 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3x%5E2%2B3x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3x%5E2%2B3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. opens up or opens down\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opens ALIGN=MIDDLE  ALT=\"opens\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+down ALIGN=MIDDLE  ALT=\"+down\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> coefficient of the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2 ALIGN=MIDDLE  ALT=\"+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative\r<BR>\n" );
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document.write( "b. vertex =\r<BR>\n" );
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document.write( "write equation in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-3x%5E2%2B3x%29-2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-3x%5E2%2B3x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%5E2-x%29-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%5E2-x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%5E2-x%2Bb%5E2%29-%28-3%29b%5E2-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%5E2-x%2Bb%5E2%29-%28-3%29b%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F2 ALIGN=MIDDLE  ALT=\"b=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%5E2-x%2B%281%2F2%29%5E2%29%2B3%281%2F2%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4%29-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4-8%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x-1%2F2%29%5E2%2B3%2F4-8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x-1%2F2%29%5E2-5%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x-1%2F2%29%5E2-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1%2F2 ALIGN=MIDDLE  ALT=\"h=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-5%2F4 ALIGN=MIDDLE  ALT=\"k=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4 ALIGN=MIDDLE  ALT=\"-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "c axis of symmetry\r<BR>\n" );
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document.write( "The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d. show algebraically how you know the function has no x-intercepts\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2B3x-2=0 ALIGN=MIDDLE  ALT=\"-3x%5E2%2B3x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.\r<BR>\n" );
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document.write( "if determinant <0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2-4%28-3%29%28-2%29%3C0 ALIGN=MIDDLE  ALT=\"3%5E2-4%28-3%29%28-2%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-24%3C0 ALIGN=MIDDLE  ALT=\"9-24%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%3C0 ALIGN=MIDDLE  ALT=\"-15%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >->proven\r<BR>\n" );
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document.write( "e. internal where it is increasing and decreasing<BR>\n" );
document.write( "in interval (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is increasing ,and in interval (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >) decreasing\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%281%2F2%2C-5%2F4%2C.12%29%2Clocate%281%2F2%2C-5%2F4%2Cv%281%2F2%2C-5%2F4%29%29%2C+green%28line%281%2F2%2C10%2C1%2F2%2C-10%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%5E2%2B3x-2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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