document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65159>Question 65159</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072918861/algebrahomeworkh>algebra for college students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "how do i fint the vertex and intercepts for this quadratic function:\r<BR>\n" );
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document.write( "f(x) = x^2 - 6x\r<BR>\n" );
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document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45650 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=45650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^2 - 6x<BR>\n" );
document.write( "There are a couple of ways to find the vertex, if your teacher is putting the equation in vertex form, let me know and I'll redo this.<BR>\n" );
document.write( "When a quadratic equation is in this form: f(x)=ax^2+bx+c, I prefer using this formula to find the x coordinate of the vertex:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-b%2F2a%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=1, b=-6 and c=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28-6%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x=-%28-6%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2F2 ALIGN=MIDDLE  ALT=\"x=6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "To find the y-coordinate find f(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%283%29%5E2-6%283%29 ALIGN=MIDDLE  ALT=\"f%283%29=%283%29%5E2-6%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=9-18 ALIGN=MIDDLE  ALT=\"f%283%29=9-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=-9 ALIGN=MIDDLE  ALT=\"f%283%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex (x,y)=(3,-9)<BR>\n" );
document.write( "You find the y-intercept, by letting x=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280%29%5E2-6%280%29 ALIGN=MIDDLE  ALT=\"f%280%29=%280%29%5E2-6%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0-0 ALIGN=MIDDLE  ALT=\"f%280%29=0-0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0 ALIGN=MIDDLE  ALT=\"f%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercept is (0,0)  The origin will be both an x and a y-intercept.<BR>\n" );
document.write( "To find the x-intercept, let f(x)=0 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-6x ALIGN=MIDDLE  ALT=\"0=x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28x-6%29 ALIGN=MIDDLE  ALT=\"0=x%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=0 and x-6=0<BR>\n" );
document.write( "x=0 and x=6<BR>\n" );
document.write( "The x-intercepts are (0,0) and (6,0)<BR>\n" );
document.write( "Here's what it looks like:<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%5E2-6x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );