document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34600>Question 34600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the parabola: y=x^2-6x+5.<BR>\n" );
document.write( "	(i)  Complete the square.<BR>\n" );
document.write( "	(ii)  Give the Vertex.<BR>\n" );
document.write( "	(iii)  Give the x- and y-intercepts.<BR>\n" );
document.write( "	(iv)  Graph the parabola.<BR>\n" );
document.write( "I have been working on this one but cannot get it right.  Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20880 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2-6x+5=y<BR>\n" );
document.write( "(x^2-6x   =y-5<BR>\n" );
document.write( "Complete the square on the left side and maintain the equal sign, as follows;<BR>\n" );
document.write( "x^2-6x+3^2 = y-5+3^2<BR>\n" );
document.write( "Factor the left side and simplify the right side to get:<BR>\n" );
document.write( "(x-3)^2 = y+4<BR>\n" );
document.write( "a)  The vertex is (3,-4)<BR>\n" );
document.write( "b)  To get the x-intercept, let y=0. Then<BR>\n" );
document.write( "  x^2-6x+5=0<BR>\n" );
document.write( " (x-5)(x-1)=0<BR>\n" );
document.write( " x=5 or x=1  (these are the x-intercepts<BR>\n" );
document.write( "c) To get the y-intercept, let x=0<BR>\n" );
document.write( "0^2-6(0)+5=y<BR>\n" );
document.write( "y=5  This is the y intercept.<BR>\n" );
document.write( "d) Graph as follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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-6x%2B5+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-6x%2B5+=+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=%28-6%29%5E2-4%2A1%2A5=16 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-6%29%5E2-4%2A1%2A5=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=16 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--6%2B-sqrt%28+16+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--6%2B-sqrt%28+16+%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-%28-6%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+5\"   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-%28-6%29-sqrt%28+16+%29%29%2F2%5C1+=+1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-6%29-sqrt%28+16+%29%29%2F2%5C1+=+1\"   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-6x%2B5 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-6x%2B5\"   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-6x%2B5+=+1%28x-5%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-6x%2B5+=+1%28x-5%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5, 1.\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-6%2Ax%2B5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );