document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148000>Question 148000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex and intercepts for this parabola:\r<BR>\n" );
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document.write( "g(x) = x^2 + x - 6\r<BR>\n" );
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document.write( "This is how I have worked it:<BR>\n" );
document.write( "a = 1, b = 1, c = -6\r<BR>\n" );
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document.write( "x = -b/2a<BR>\n" );
document.write( "x = -1/[2(1)] = -1/2\r<BR>\n" );
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document.write( "g(-1/2) = (-1/2)^2 + (-1/2) - 6<BR>\n" );
document.write( "= 25/2\r<BR>\n" );
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document.write( "So, the vertex is (-1/2, 25/2)\r<BR>\n" );
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document.write( "Am I correct so far?\r<BR>\n" );
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document.write( "How do I verify that I am correct? What should my next step be?\r<BR>\n" );
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document.write( "I appreciate your help very much!  Thank you!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108389 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=108389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font size=4><b>Vertex:</b></font>\r<BR>\n" );
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document.write( "In order to find the vertex, we first need to find the x-coordinate of the vertex.\r<BR>\n" );
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document.write( "To find the x-coordinate of the vertex, use this formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula.\r<BR>\n" );
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document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%281%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x=%28-%281%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x=%28-1%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: this means that the axis of symmetry is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29%5E2-1%2F2-6 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29%5E2-1%2F2-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F2%29%5E2-1%2F2-6 ALIGN=MIDDLE  ALT=\"y=%28-1%2F2%29%5E2-1%2F2-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F4-1%2F2-6 ALIGN=MIDDLE  ALT=\"y=1%2F4-1%2F2-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-25%2F4 ALIGN=MIDDLE  ALT=\"y=-25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\frac{1}{2},-\frac{25}{4}\right)\">\r<BR>\n" );
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document.write( "note: you can verify this with a calculator. You can use the \"min/max\" feature. \r<BR>\n" );
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document.write( "<font size=4><b>Intercepts:</b></font>\r<BR>\n" );
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document.write( "x-intercept:\r<BR>\n" );
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document.write( "To find the x-intercept, plug in <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;\" > and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"0=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-2%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Now solve for x in each case\r<BR>\n" );
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document.write( "So the x-intercepts are (-3,0) and (2,0)\r<BR>\n" );
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document.write( "y-intercept:\r<BR>\n" );
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document.write( "To find the y-intercept, plug in <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;\" > and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%5E2%2B0-6 ALIGN=MIDDLE  ALT=\"y=0%5E2%2B0-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "<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;\" > Simplify\r<BR>\n" );
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document.write( "So the y-intercept is (0,-6) \r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx-6 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  we can visually verify our answers.\r<BR>\n" );
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