document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55410>Question 55410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the maximum (or minimum) of each function, also determine the x-intercepts of each function (if any). Express your final answers as a decimal number (rounded to 4 decimal places if necessary) \r<BR>\n" );
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document.write( "a. f(x)= x2-2x-3 \r<BR>\n" );
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document.write( "(this is what i came up with so far)\r<BR>\n" );
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document.write( "a=1<BR>\n" );
document.write( "b=-2  h= -b/2a= 2/2= 1 <BR>\n" );
document.write( "c=-3\r<BR>\n" );
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document.write( "I don't think this is right i need your help!!\r<BR>\n" );
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document.write( "b. F(x)= -x2+2x+3 <BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "b=3  h=-b/2a= -(-2)/2(-1)=1<BR>\n" );
document.write( "c=3\r<BR>\n" );
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document.write( "same thing here...I'm not sure what to do here... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37637 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=37637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the maximum (or minimum) of each function, also determine the x-intercepts of each function (if any). Express your final answers as a decimal number (rounded to 4 decimal places if necessary) \r<BR>\n" );
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document.write( "a. f(x)= x^2-2x-3 <BR>\n" );
document.write( "a=1 (Because a is positive the parabola is a u shape and it's vertex is a minimum.<BR>\n" );
document.write( "b=-2  <BR>\n" );
document.write( "c=-3<BR>\n" );
document.write( "To find the vertex:<BR>\n" );
document.write( "x= -b/2a= 2/2= 1 Plug this value in to find the height:<BR>\n" );
document.write( "f(1)=(1)^2-2(1)-3<BR>\n" );
document.write( "f(1)=1-2-3=-4<BR>\n" );
document.write( "The minimum value is at the point (1,-4)<BR>\n" );
document.write( "The x-intercepts happen when f(x)=0<BR>\n" );
document.write( "0=x^2-2x-3 Factor.<BR>\n" );
document.write( "0=(x___)(x____)<BR>\n" );
document.write( "Two numbers that multiply to give you -3 (c) but add together to give you -2 (b) are: -3 and +1<BR>\n" );
document.write( "0=(x-3)(x+1)  Use the zero product property and set each parenthesis = 0 and solve for x.<BR>\n" );
document.write( "x-3=0 and x+1=0<BR>\n" );
document.write( "x=3 and x=-1<BR>\n" );
document.write( "The x intercepts are (-1,0) and (3,0).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. F(x)= -x2+2x+3 <BR>\n" );
document.write( "a=-1 a is negative so the parabola is n shaped and its vertex is it's maximun point.<BR>\n" );
document.write( "b=2  <BR>\n" );
document.write( "c=3<BR>\n" );
document.write( "To find the vertex:<BR>\n" );
document.write( "x=-b/2a= -(2)/2(-1)=1<BR>\n" );
document.write( "F(1)=-(1)^2+2(1)+3<BR>\n" );
document.write( "F(1)=-1+2+3=4<BR>\n" );
document.write( "The maximum point is at the vertex:(1,4)<BR>\n" );
document.write( "The x-intercepts happen when y=0<BR>\n" );
document.write( "0=-x^2+2x+3<BR>\n" );
document.write( "-(0)=-(-x^2+2x+3)<BR>\n" );
document.write( "0=x^2-2x-3  The same as the first parabola so it's x intercepts are also:(-1,0) and (3,0).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Together they look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-3%2C-x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-3%2C-x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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