document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187844>Question 1187844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the quadratic function:<BR>\n" );
document.write( "f(x) = -1/2x^2-3x+5/2\r<BR>\n" );
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document.write( "a. Determine whether the parabola opens up or opens down.<BR>\n" );
document.write( "b. Find the vertex of the parabola.<BR>\n" );
document.write( "c. Determine the axis of the symmetry.<BR>\n" );
document.write( "d. Find the x  -  intercepts and the y  -  intercept of the parabola.<BR>\n" );
document.write( "e. Sketch the graph of f(x). </SPAN>\n" );
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document.write( "Given the quadratic function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-%281%2F2%29x%5E2-3x%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29x%5E2-3x%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. Determine whether the parabola opens up or opens down.\r<BR>\n" );
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document.write( "if the leading coefficient is less than zero, as in your case, <BR>\n" );
document.write( "the parabola opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=down ALIGN=MIDDLE  ALT=\"down\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Find the vertex of the parabola.\r<BR>\n" );
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document.write( "rewrite 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-%281%2F2%29x%5E2-3x%29%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28-%281%2F2%29x%5E2-3x%29%2B5%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+=+-%281%2F2%29%28x%5E2%2B6x%29%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29%28x%5E2%2B6x%29%2B5%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+=+-%281%2F2%29%28x%5E2%2B6x%2Bb%5E2%29-%28-1%2F2%29b%5E2%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29%28x%5E2%2B6x%2Bb%5E2%29-%28-1%2F2%29b%5E2%2B5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6%2F2=3 ALIGN=MIDDLE  ALT=\"b=6%2F2=3\"   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+=+-%281%2F2%29%28x%5E2%2B6x%2B3%5E2%29%2B%281%2F2%293%5E2%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29%28x%5E2%2B6x%2B3%5E2%29%2B%281%2F2%293%5E2%2B5%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+=+-%281%2F2%29%28x%2B3%29%5E2%2B9%2F2%2B5%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29%28x%2B3%29%5E2%2B9%2F2%2B5%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+=+-%281%2F2%29%28x%2B3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29%28x%2B3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-3 ALIGN=MIDDLE  ALT=\"h=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=7 ALIGN=MIDDLE  ALT=\"k=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "c. Determine the axis of the symmetry.\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > -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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d. Find the x - intercepts and the y - intercept of the parabola.\r<BR>\n" );
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document.write( "x - intercepts: set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=0 ALIGN=MIDDLE  ALT=\"f%28x%29+=0\"   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=0+=+-%281%2F2%29%28x%2B3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"0+=+-%281%2F2%29%28x%2B3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=+%281%2F2%29%28x%2B3%29%5E2=7 ALIGN=MIDDLE  ALT=\"+%281%2F2%29%28x%2B3%29%5E2=7\"   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=+%28x%2B3%29%5E2=7%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"+%28x%2B3%29%5E2=7%2F%281%2F2%29\"   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=+%28x%2B3%29%5E2=14 ALIGN=MIDDLE  ALT=\"+%28x%2B3%29%5E2=14\"   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=+x%2B3=sqrt%2814%29 ALIGN=MIDDLE  ALT=\"+x%2B3=sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=sqrt%2814%29+-3 ALIGN=MIDDLE  ALT=\"+x=sqrt%2814%29+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++sqrt%2814%29-3 ALIGN=MIDDLE  ALT=\"x+=++sqrt%2814%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7 ALIGN=MIDDLE  ALT=\"0.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++-+sqrt%2814%29-3 ALIGN=MIDDLE  ALT=\"x+=++-+sqrt%2814%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6.7 ALIGN=MIDDLE  ALT=\"-6.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y - intercepts: set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=0 ALIGN=MIDDLE  ALT=\"x+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=y ALIGN=MIDDLE  ALT=\"f%28x%29=y\"   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=y=+-%281%2F2%29%280%2B3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"y=+-%281%2F2%29%280%2B3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+5%2F2 ALIGN=MIDDLE  ALT=\"y=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e. Sketch the graph of f(x).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%281%2F2%29%28x%2B3%29%5E2%2B7%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%281%2F2%29%28x%2B3%29%5E2%2B7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );