document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177829>Question 177829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quadratic Equations<BR>\n" );
document.write( "Complete the square to rewrite each relation in the form y=a(x-h)^2+k. Then, sketch a graph of each parabola, labelling the vertex, the axis of symmetry, and two other points.<BR>\n" );
document.write( "a)y=x^2+4x+10<BR>\n" );
document.write( "b)y=-x^2+6x-8<BR>\n" );
document.write( "c)y=-2x^2-12x-7<BR>\n" );
document.write( "Thank you very much<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133501 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=133501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> </pre><font size=4><b><BR>\n" );
document.write( "a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B4x%2B10 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B4x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B4x%2B4%29%2B10-4 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B4x%2B4%29%2B10-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%28x%2B2%29%5E2%2B6%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%28x%2B2%29%5E2%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Vertex: (-2,6)<BR>\n" );
document.write( "Axis of Symmetry=-2<BR>\n" );
document.write( "Solving the X-intercepts:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--->where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=4%2Cc=10%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=4%2Cc=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving the Discriminant: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=4%5E2-4%2A1%2A10=16-40=-24 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=4%5E2-4%2A1%2A10=16-40=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >---> since negative, it has no solutions for real numbers.<BR>\n" );
document.write( "Y-Intercept: <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%5E2%2B4%280%29%2B10 ALIGN=MIDDLE  ALT=\"y=0%5E2%2B4%280%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10 ALIGN=MIDDLE  ALT=\"y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Continuing,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B-i%2Asqrt%28-24%29%29%2F%282%2A1%29=%28-4%2B-i%2A4.8989795%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-4%2B-i%2Asqrt%28-24%29%29%2F%282%2A1%29=%28-4%2B-i%2A4.8989795%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or see the graph,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-8%2C5%2C-5%2C20%2Cgrid%281%29%2Cgraph%28400%2C400%2C-8%2C5%2C-5%2C20%2Cx%5E2%2B4x%2B10%29%2Cgreen%28line%28-2%2C20%2C-2%2C-5%29%29%2Ccircle%28-2%2C6%2C.15%29%2Ccircle%280%2C10%2C.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2B6x-8 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B6x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%28x%5E2%2B6x-8%29 ALIGN=MIDDLE  ALT=\"y=-1%28x%5E2%2B6x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%28x%5E2%2B6x%2B9%29%2B8-9 ALIGN=MIDDLE  ALT=\"y=-1%28x%5E2%2B6x%2B9%29%2B8-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-1%28x-3%29%5E2-1%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-1%28x-3%29%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28h=x=3%2Ck=y=highlight%281%29%29 ALIGN=MIDDLE  ALT=\"system%28h=x=3%2Ck=y=highlight%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, highlighted: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ak=%28-1%29%28-1%29=1 ALIGN=MIDDLE  ALT=\"a%2Ak=%28-1%29%28-1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, oks!<BR>\n" );
document.write( "Vertex: (3,1)<BR>\n" );
document.write( "Axis of Symmetry: =3<BR>\n" );
document.write( "Remember<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=-1%2Cb=6%2Cc=-8%29 ALIGN=MIDDLE  ALT=\"system%28a=-1%2Cb=6%2Cc=-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for Discriminant: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=6%5E2-4%2A%28-1%29%28-8%29=36-32=4 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=6%5E2-4%2A%28-1%29%28-8%29=36-32=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-highlight%28sqrt%28b%5E2-4ac%29%29%29%2F%282a%29=%28-6%2B-sqrt%284%29%29%2F%282%2A-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6%2B-2%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-6%2B-2%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6%2B2%29%2F-2=-4%2F-2=2 ALIGN=MIDDLE  ALT=\"x=%28-6%2B2%29%2F-2=-4%2F-2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6-2%29%2F-2=-8%2F-2=4 ALIGN=MIDDLE  ALT=\"x=%28-6-2%29%2F-2=-8%2F-2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "X-Intercepts<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=2%2Cx=4%29 ALIGN=MIDDLE  ALT=\"system%28x=2%2Cx=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Y-Intercept: <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%280%29%5E2%2B6%280%29-8 ALIGN=MIDDLE  ALT=\"y=-%280%29%5E2%2B6%280%29-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We'll see the graph,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-6%2C6%2C-10%2C6%2Cgrid%281%29%2Cgraph%28400%2C400%2C-6%2C6%2C-10%2C6%2C-x%5E2%2B6x-8%29%2Ccircle%282%2C0%2C.12%29%2Ccircle%284%2C0%2C.12%29%2Cgreen%28line%283%2C6%2C3%2C-10%29%29%2C+blue%28circle%280%2C-8%2C.12%29%29%2Ccircle%283%2C1%2C.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%5E2-12x-7 ALIGN=MIDDLE  ALT=\"y=-2x%5E2-12x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%5E2%2B6x%2B7%2F2%29 ALIGN=MIDDLE  ALT=\"y=-2%28x%5E2%2B6x%2B7%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%5E2%2B6x%2B9%29%2B%287%2F2%29-9 ALIGN=MIDDLE  ALT=\"y=-2%28x%5E2%2B6x%2B9%29%2B%287%2F2%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%2B3%29%5E2%2B%287-18%29%2F2 ALIGN=MIDDLE  ALT=\"y=-2%28x%2B3%29%5E2%2B%287-18%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-2%28x%2B3%29%5E2-%2811%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-2%28x%2B3%29%5E2-%2811%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-->it follows <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28h=x=-3%2Ck=y=11%29 ALIGN=MIDDLE  ALT=\"system%28h=x=-3%2Ck=y=11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Vertex: (-3,11)------->Again, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%2Ak=-2%2A%28-11%2F2%29=11 ALIGN=MIDDLE  ALT=\"y=a%2Ak=-2%2A%28-11%2F2%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Axis 0f Symmetry= -3<BR>\n" );
document.write( "For X-Intercepts:<BR>\n" );
document.write( "Remember<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=6%2Cc=7%2F2%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=6%2Cc=7%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "WE 1st solve for the discriminant: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=6%5E2-4%2A1%2A%287%2F2%29=36-%2828%2F2%29=36-14=22 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=6%5E2-4%2A1%2A%287%2F2%29=36-%2828%2F2%29=36-14=22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-highlight%28sqrt%28b%5E2-4ac%29%29%29%2F%282a%29=%28-6%2B-sqrt%2822%29%29%2F%282%2A1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6%2B-4.69%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-6%2B-4.69%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6%2B4.69%29%2F2=-1.31%2F2=highlight%28-0.655%29 ALIGN=MIDDLE  ALT=\"x=%28-6%2B4.69%29%2F2=-1.31%2F2=highlight%28-0.655%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=%28-6-4.69%29%2F2=-10.69%2F2=highlight%28-5.345%29 ALIGN=MIDDLE  ALT=\"x=%28-6-4.69%29%2F2=-10.69%2F2=highlight%28-5.345%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Y-Intercept: <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%280%29%5E2-12%280%29-7 ALIGN=MIDDLE  ALT=\"y=-2%280%29%5E2-12%280%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We see the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-8%2C6%2C-8%2C12%2Cgrid%281%29%2Cgraph%28400%2C400%2C-8%2C6%2C-8%2C12%2C-2x%5E2-12x-7%29%2Ccircle%28-0.655%2C0%2C.15%29%2Ccircle%28-5.345%2C0%2C.15%29%2Cgreen%28line%28-3%2C12%2C-3%2C-8%29%29%2Ccircle%280%2C-7%2C.12%29%2Ccircle%28-3%2C11%2C.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo</pre>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );