document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068849>Question 1068849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a family of quadratic functions has zeros -3 and 5.Which of the following is a member of this family?<BR>\n" );
document.write( "a) y= -1/2(x+3)(x-5)<BR>\n" );
document.write( "b) y= 2(x+3)^2(x-5)<BR>\n" );
document.write( "c) y= 4(x+3)(x-5)(x+15)<BR>\n" );
document.write( "d) y=(x+5)(x-3)\r<BR>\n" );
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document.write( "draw me a graph with polynomial function  of cubic equation with roots -2,3,and 4\r<BR>\n" );
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document.write( "what are the real roots of x^4-2x^3+3x+2=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #684103 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=684103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Options b) and c) show polynomials of degree 3:<BR>\n" );
document.write( "b) y= 2(x+3)^2(x-5) an<BR>\n" );
document.write( "c) y= 4(x+3)(x-5)(x+15)<BR>\n" );
document.write( "Polynomials of degree 3 can be called \"cubic functions,\"<BR>\n" );
document.write( "but the name \"quadratic\" is reserved for polynomial of degree 2,<BR>\n" );
document.write( "like choices a) and d) :<BR>\n" );
document.write( "a) y= -1/2(x+3)(x-5)<BR>\n" );
document.write( "d) y=(x+5)(x-3) <BR>\n" );
document.write( " <BR>\n" );
document.write( "If a polynomial function has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a zero,<BR>\n" );
document.write( "its factored form will have the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If a polynomial function has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a zero,<BR>\n" );
document.write( "its factored form will have the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-3%29%29=%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-%28-3%29%29=%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in a polynomial with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a factor will make the polynomial zero.<BR>\n" );
document.write( "Substituting <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;\" > in a polynomial with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a factor will make the polynomial zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28matrix%281%2C2%2C%22a+%29%22%2Cy=+%28-1%2F2%29%28x%2B3%29%28x-5%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28matrix%281%2C2%2C%22a+%29%22%2Cy=+%28-1%2F2%29%28x%2B3%29%28x-5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "a quadratic function,<BR>\n" );
document.write( "and it has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as zeros.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "A polynomial is not allowed to have more zeros than its grade.<BR>\n" );
document.write( "A polynomial of degree 2,<BR>\n" );
document.write( "such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B5%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B5%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "can have at most 2 zeros.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B5%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B5%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "gives you <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;\" > ,<BR>\n" );
document.write( "so obviously the zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B5%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B5%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );