document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=701011>Question 701011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me. I don't understand how to start these. \r<BR>\n" );
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document.write( "1. For the given equation, list the intercepts and test for symmetry.<BR>\n" );
document.write( "y=x^2-5x-6\r<BR>\n" );
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document.write( "2. Write the equation of the circle in standard form.  Find the center, radius, intercepts, and graph the<BR>\n" );
document.write( "circle.<BR>\n" );
document.write( "x^2+y^2+14x-12y=-76 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432220 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=432220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-5x-6 ALIGN=MIDDLE  ALT=\"y=x%5E2-5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be called a quadratic function and graphs as a parabola opening up. (It's shaped like a smile).<BR>\n" );
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document.write( "Intercepts are the points where the graph representing that equation crosses the x-axis and the y-axis.<BR>\n" );
document.write( "The x-axis is the set of all the points with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find the x-intercepts:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-5x-6 ALIGN=MIDDLE  ALT=\"0=x%5E2-5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-6%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"0=%28x-6%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (factoring)<BR>\n" );
document.write( "has a solution when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6=0 ALIGN=MIDDLE  ALT=\"x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight+%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight+%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "a solution when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-axis is the set of all the points with <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;\" > .<BR>\n" );
document.write( "Making <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;\" > we find the y-intercept:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%5E2-5%2A0-6 ALIGN=MIDDLE  ALT=\"y=0%5E2-5%2A0-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0-1-6 ALIGN=MIDDLE  ALT=\"y=0-1-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-6%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "When teachers say to test for SYMMETRY they usually want you to find out, without graphing,<BR>\n" );
document.write( "if the graph representing the equation has symmetry.<BR>\n" );
document.write( "Maybe the side to the right of the y-axis is a mirror image of the left side.<BR>\n" );
document.write( "Or maybe the side above of the x-axis is a mirror image of side below the x-axis.<BR>\n" );
document.write( "Or maybe every point has a reflection on the other side of the origin.<BR>\n" );
document.write( "To find out, you change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y ALIGN=MIDDLE  ALT=\"-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or (x,y) to (-x,-y),<BR>\n" );
document.write( "and see if you end up with the same equation.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-5x-6 ALIGN=MIDDLE  ALT=\"y=x%5E2-5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, any of those changes gives you a different equation.<BR>\n" );
document.write( "The graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-5x-6 ALIGN=MIDDLE  ALT=\"y=x%5E2-5x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > has an axis of symmetry, but it is neither the x-axis, not the y-axis.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Knowing that a graph will be symmetrical before you start graphing, makes graphing easier.<BR>\n" );
document.write( "In pictures,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28100%2C100%2C-5%2C5%2C-5%2C5%2Cx%5E2%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28100%2C100%2C-5%2C5%2C-5%2C5%2Cx%5E2%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a function with symmetry about the y-axis because it has the same y 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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( f(x)=f(-x) }<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2By%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2By%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > graphs as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28100%2C100%2C-2%2C8%2C-5%2C5%2Cgrid%281%29%2Cblue%28circle%283%2C0%2C3%29%29%29 ALIGN=MIDDLE  ALT=\"drawing%28100%2C100%2C-2%2C8%2C-5%2C5%2Cgrid%281%29%2Cblue%28circle%283%2C0%2C3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and has symmetry about the x-axis, because for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y ALIGN=MIDDLE  ALT=\"-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > the equation is the same.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28100%2C100%2C-6%2C6%2C-6%2C6%2Cgrid%281%29%2Cblue%28circle%280%2C0%2C4%29%29%29 ALIGN=MIDDLE  ALT=\"drawing%28100%2C100%2C-6%2C6%2C-6%2C6%2Cgrid%281%29%2Cblue%28circle%280%2C0%2C4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=1 ALIGN=MIDDLE  ALT=\"xy=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C1%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28100%2C100%2C-5%2C5%2C-5%2C5%2C1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "have symmetry about the origin because the equation is the same for point (x,y) as for point (-x,-y).<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B14x-12y=-76 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B14x-12y=-76\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B14x%2By%5E2-12y=-76 ALIGN=MIDDLE  ALT=\"x%5E2%2B14x%2By%5E2-12y=-76\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B14x%2B49%2By%5E2-12y%2B36=-76%2B49%2B36 ALIGN=MIDDLE  ALT=\"x%5E2%2B14x%2B49%2By%5E2-12y%2B36=-76%2B49%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B14x%2B49%29%2B%28y%5E2-12y%2B36%29=9 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B14x%2B49%29%2B%28y%5E2-12y%2B36%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x%2B7%29%5E2%2B%28y-6%29%5E2=3%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x%2B7%29%5E2%2B%28y-6%29%5E2=3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That equation is true for all the points (x,y) that are at distance 3 from point (-7,6).<BR>\n" );
document.write( "That is the equation of a circle with radius 3, centered at the point (-7,6),<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The center is too far below the x-axis compared to the radius, so the circle does not cross the x-axis, and there are no x-intercepts.<BR>\n" );
document.write( "The same thing happens with the y-axis. The center is too far to the right. There is no y-intercept. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );