document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=590300>Question 590300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help me.\r<BR>\n" );
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document.write( "write an equation and graph it\r<BR>\n" );
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document.write( "1.) A quadratic function with x-intercept (3,0)and(-6,0)and y-intercept (0,-5)\r<BR>\n" );
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document.write( "5.) A cubic function with x-intercept (1,0)(-1/2,0)and(1/4,0)and y-intercept(0,2)\r<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 #375128 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=375128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.)<BR>\n" );
document.write( "A quadratic polynomial with zeros at x=3 and x=-6, must have (x-3) and (x+6) as factors (and no other factor involving x).<BR>\n" );
document.write( "So, it would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=K%28x-3%29%28x%2B6%29=K%28x%5E2%2B3x-18%29 ALIGN=MIDDLE  ALT=\"y=K%28x-3%29%28x%2B6%29=K%28x%5E2%2B3x-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some non-zero number K.<BR>\n" );
document.write( "For x=0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-18K=-5 ALIGN=MIDDLE  ALT=\"y=-18K=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=5%2F18 ALIGN=MIDDLE  ALT=\"K=5%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F18%29%28x-3%29%28x%2B6%29=%285%2F18%29%28x%5E2%2B3x-18%29=%285%2F18%29x%5E2%2B%285%2F6%29x-5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > is your function.<BR>\n" );
document.write( "You know the graph is a prabola, you know the intercepts,and you know that it opens up because the leading coefficient (5/18) is positive.<BR>\n" );
document.write( "The axis of symmetry of the parabola has to be exactly halfway between its zeros, at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283-6%29%2F2=-3%2F2 ALIGN=MIDDLE  ALT=\"x=%283-6%29%2F2=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The minimum (vertex) of the parabola has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%285%2F18%29+%28-3%2F2-3%29%28-3%2F2%2B6%29=%285%2F18%29%28-9%2F2%29%289%2F2%29=-5%2A9%2A9%2F%2818%2A2%2A2%29=-45%2F8=-5%265%2F8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graphing parabolas, with all that information is easy.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-9%2C6%2C-10%2C10%2C%285%2F18%29%28x-3%29%28x%2B6%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-9%2C6%2C-10%2C10%2C%285%2F18%29%28x-3%29%28x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "2.) For the second function it would be<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=K%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29 ALIGN=MIDDLE  ALT=\"y=K%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We do not need to do the whole multiplication to figure out that the independent term (you may call it constant) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%28-1%2F2%29%2A%281%2F4%29K=%281%2F8%29K ALIGN=MIDDLE  ALT=\"%28-1%29%28-1%2F2%29%2A%281%2F4%29K=%281%2F8%29K\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For x=0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F8%29K=2 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29K=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> K=16<BR>\n" );
document.write( "The function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29 ALIGN=MIDDLE  ALT=\"y=16%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Its zeros are -1/2, 1/4 and 1, and are the points were it changes sign.<BR>\n" );
document.write( "It is negative for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1%2F2 ALIGN=MIDDLE  ALT=\"x%3C-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "positive for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2%3Cx%3C1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F2%3Cx%3C1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (including x=0, where y=2),<BR>\n" );
document.write( "negative for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%3Cx%3C1 ALIGN=MIDDLE  ALT=\"1%2F4%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and positive for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " GRAPHING:<BR>\n" );
document.write( "Depending on what you are being taught in class is how you would graph the function in problem 2.<BR>\n" );
document.write( "If they are teaching you the use of a graphing calculator or some graphing program, you would use that.<BR>\n" );
document.write( "If your class is calculus, you would find the derivative, and locate maxima and minima.<BR>\n" );
document.write( "Otherwise, you may calculate the value of the function for a few values of x (maybe x=-1, x=1/2, and x=2), plot those points and the intercepts, and sketch a curve that reasonable passes through all those points.<BR>\n" );
document.write( "This website will graph for me.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-1%2C3%2F2%2C-15%2C20%2C16%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-1%2C3%2F2%2C-15%2C20%2C16%28x-1%29%28x%2B1%2F2%29%28x-1%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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