document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256575>Question 256575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a parabola question. I really need help solving. if you could please show me the work and also tell me how to solve. thank you! :)\r<BR>\n" );
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document.write( "without drawing the graph of the given equation determine<BR>\n" );
document.write( "A) how many x-intercepts the parabola has<BR>\n" );
document.write( "B) whether its vertex lies above or below or on the x-axis.<BR>\n" );
document.write( "show your work.\r<BR>\n" );
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document.write( "1) y=x(squared) - 5x +6\r<BR>\n" );
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document.write( "2) y= -x(squared) + 2x -1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188662 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It would help if you put more time into copying the question correctly and less time crying.<BR>\n" );
document.write( "Notice how squared is correctly written. Notice how 1) appears by enclosing the problem in three \"{\" and  three \"}\" curly braces. Next to the p key<BR>\n" );
document.write( "1)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x%5E2-5x%2B6 ALIGN=MIDDLE  ALT=\"+y=x%5E2-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) y=-x^2+2x-1<BR>\n" );
document.write( "The rules of the website say <BR>\n" );
document.write( "One problem per submission.<BR>\n" );
document.write( "No similar problems and<BR>\n" );
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document.write( "You broke two of the rules already.<BR>\n" );
document.write( "One and two are similar and are two problems.<BR>\n" );
document.write( "Whereas A and B can be considered one problem<BR>\n" );
document.write( "Here is the solution to 1)<BR>\n" );
document.write( "The determinant tells how many  x roots there are. <BR>\n" );
document.write( "See description below<BR>\n" );
document.write( "vertex lowest point (5/2,  -1/4) slightly below the x axis<BR>\n" );
document.write( "the x of the vertex is -b/2a find that and plug it in to find y<BR>\n" );
document.write( "-(-)5/2(1)=5/2<BR>\n" );
document.write( "plug 5/2 for x and get -1/4 for y in<BR>\n" );
document.write( " y=x^2-5x+6<BR>\n" );
document.write( " y=5/2^2-5*5/2+6<BR>\n" );
document.write( "y=25/4-25/2+24/4<BR>\n" );
document.write( "y=(25-50+24)/4<BR>\n" );
document.write( "y=-1/4\r<BR>\n" );
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document.write( "BTW y=x^2-5x+6 can be factored into y=(x-3)(x-2)<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B6+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-5%29%5E2-4%2A1%2A6=1 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A1%2A6=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--5%2B-sqrt%28+1+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+1+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-5%29-sqrt%28+1+%29%29%2F2%5C1+=+2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5%29-sqrt%28+1+%29%29%2F2%5C1+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B6 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B6+=+1%28x-3%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6+=+1%28x-3%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, 2.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );