document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127701>Question 127701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Can I have some help concerning this problem?\r<BR>\n" );
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document.write( "Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. \r<BR>\n" );
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document.write( "y = 6x^2 + 7x + 1 \r<BR>\n" );
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document.write( "	(vertex)<BR>\n" );
document.write( "y =	(y-intercept)<BR>\n" );
document.write( "x = 	(leftmost x-intercept)<BR>\n" );
document.write( "x = 	 (rightmost x-intercept) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93596 by </B><A HREF=/tutors/aboutme.mpl?userid=JessicaGill><B>JessicaGill(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JessicaGill><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=93596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Using the quadratic solver here are the steps\r<BR>\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=6x%5E2%2B7x%2B1+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B7x%2B1+=+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=%287%29%5E2-4%2A6%2A1=25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%287%29%5E2-4%2A6%2A1=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=25 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+=+%28-7%2B-sqrt%28+25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-7%2B-sqrt%28+25+%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-%287%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+-0.166666666666667 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%287%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+-0.166666666666667\"   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-%287%29-sqrt%28+25+%29%29%2F2%5C6+=+-1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%287%29-sqrt%28+25+%29%29%2F2%5C6+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B7x%2B1 ALIGN=MIDDLE  ALT=\"6x%5E2%2B7x%2B1\"   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=6x%5E2%2B7x%2B1+=+6%28x--0.166666666666667%29%2A%28x--1%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B7x%2B1+=+6%28x--0.166666666666667%29%2A%28x--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.166666666666667, -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+6%2Ax%5E2%2B7%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B7%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "You can also use the vertex formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28b%2F2a%29 ALIGN=MIDDLE  ALT=\"x=-%28b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the x coordinate of the vertex and the axis of symmetry.  Once you find the x value, substitute the value for x in the original equation and find the y coordinate of the vertex.\r<BR>\n" );
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document.write( "Then choose two x values either two the left or the right of the vertex and sustitute and solve for the y coordinates to the x values.  \r<BR>\n" );
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document.write( "Then graph the reflection of each of those points and graph the parabola points and sketch the graph.  You will have to estimate the points from the graph above. </SPAN>\n" );
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