document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208807>Question 1208807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 1\r<BR>\n" );
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document.write( "(a) Write the function f(x) = 2x ^ 2 - 7x - 10 where x ∈ R, in the form a * (x + h) ^ 2 + k_{i} where a, h, and k \in\r<BR>\n" );
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document.write( " Qb) Hence, write the minimum point of f\r<BR>\n" );
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document.write( "(c) (i) Explain why / must have two real roots.\r<BR>\n" );
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document.write( "(ii) Write the roots of f(x) = 0 in the form p plus/minus sqrt(q) where p and q \in \mathbb{Q} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847314 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=847314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%28x%5E2-7x%2F2-5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%28x%5E2-7x%2F2-5%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=2%28x%5E2-7x%2F2%2B%287%2F4%29%5E2-%287%2F4%29%5E2-5%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-7x%2F2%2B%287%2F4%29%5E2-%287%2F4%29%5E2-5%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=2%28%28x-7%2F4%29%5E2-49%2F16-5%29 ALIGN=MIDDLE  ALT=\"2%28%28x-7%2F4%29%5E2-49%2F16-5%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=2%28x-7%2F4%29%5E2-49%2F8-10 ALIGN=MIDDLE  ALT=\"2%28x-7%2F4%29%5E2-49%2F8-10\"   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=2%28x-7%2F4%29%5E2-129%2F8 ALIGN=MIDDLE  ALT=\"2%28x-7%2F4%29%5E2-129%2F8\"   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=highlight%282%28x-7%2F4%29%5E2-16%261%2F8%29 ALIGN=MIDDLE  ALT=\"highlight%282%28x-7%2F4%29%5E2-16%261%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertex here will be the lowest point of the graph<BR>\n" );
document.write( "which is at  (1&3/4, -16&1/8).  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=7%2F4 ALIGN=MIDDLE  ALT=\"h=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-16%261%2F8 ALIGN=MIDDLE  ALT=\"k=-16%261%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If solve f(x) equated at 0, then you find the roots.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-7%2F4%29%5E2-16%261%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x-7%2F4%29%5E2-16%261%2F8=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=2%28x-7%2F4%29%5E2=129%2F8 ALIGN=MIDDLE  ALT=\"2%28x-7%2F4%29%5E2=129%2F8\"   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-7%2F4%29%5E2=129%2F16 ALIGN=MIDDLE  ALT=\"%28x-7%2F4%29%5E2=129%2F16\"   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-7%2F4=0%2B-+sqrt%28129%29%2F4 ALIGN=MIDDLE  ALT=\"x-7%2F4=0%2B-+sqrt%28129%29%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=highlight%28x=7%2F4%2B-+sqrt%28129%29%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=7%2F4%2B-+sqrt%28129%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the roots </SPAN>\n" );
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