document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050231>Question 1050231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Analyze the graph of the quadratic function. (The graph pictured is a parabola, pointing upward with its minimum in quadrant 2, left side mostly in quadrant 4, right side mostly in quadrant 1, and the minimum in quadrant 2 is slightly to the right of the y axis. \r<BR>\n" );
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document.write( "The standard form of a quadratic function is f(x) = ax^2 + bx + c. What possible values can a and c have for the given quadratic function Explain your reasoning. \r<BR>\n" );
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document.write( "If the vertex from of a quadratic function is f (x) = a(x-h)^2 +k...what possible value can a, h, and k have for the given quadratic function. Epxlain your reasoning. \r<BR>\n" );
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document.write( "If the factored form of a quadratic function is f (x) + a(x-r')(x-r\")...what possible values can a,r' and r\" have? explain your reasoning. <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 #665795 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=665795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The description is inconsistent and therefore makes no sense.  Look at your graph carefully again and adjust your description.  Is the vertex a minimum or a maximum?  What quadrant is it in, or if not, on which part of which axis is it?  In which quadrants are/is the left branch of the parabola?  In which quadrant is/are the right branch of the parabola?\r<BR>\n" );
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document.write( "Your adjusted description:<BR>\n" );
document.write( "The graph pictured is a parabola, pointing upward with its minimum/vertex in quadrant 4, left side mostly in quadrant 2, right side mostly in quadrant 1, and the minimum in quadrant 4 is slightly to the right of the y axis. \r<BR>\n" );
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document.write( "The graph will cross the x-axis in two places.  One at a negative x value and the other at a positive x value.  The minimum being in quadrant 4 means that the k value is negative.  The parabola having a MINIMUM for its vertex means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let me use roots r and s for the roots or x-axis intercepts, and using your factored form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-r%29%28x-s%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-r%29%28x-s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----------- this is one of the typical formats for a quadratic function.\r<BR>\n" );
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document.write( "Using that form and your parabola as described,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%3E0%2Cr%3E0%2Cs%3C0%29 ALIGN=MIDDLE  ALT=\"system%28a%3E0%2Cr%3E0%2Cs%3C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you can take the r and s variables to help in their meaning as r for RIGHTMOST, and s for SINISTER (meaning to the left or leftmost).\r<BR>\n" );
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document.write( "Also according to how you described, <i>the minimum in quadrant 4 is slightly to the right of the y axis</i>, indicates that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29%3Eabs%28s%29 ALIGN=MIDDLE  ALT=\"abs%28r%29%3Eabs%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3Cr ALIGN=MIDDLE  ALT=\"s%3Cr\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (but do not becomes confused about order and size).\r<BR>\n" );
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document.write( "You can understand this parabola and the values according to the standard form  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The vertex would be (h,k), and here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C0 ALIGN=MIDDLE  ALT=\"k%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%3E0 ALIGN=MIDDLE  ALT=\"h%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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