document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60013>Question 60013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> help on this graph needed, please! <BR>\n" );
document.write( "For the quadratic function   y= f(x)= x^2-2x-15, find the vertex and x and y intercepts. Sketch the graph, and state the domain and range.<BR>\n" );
document.write( "thanks again, carol </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41219 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=41219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi Carol,<BR>\n" );
document.write( ": <BR>\n" );
document.write( "For the quadratic function   y= f(x)= x^2-2x-15, find the vertex and x and y intercepts. Sketch the graph, and state the domain and range.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can find the x coordinate of the vertex of a parabola when the quadratic equation is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with the formula <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( "Your a=1, b=-2, and c=-15<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%28-2%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x=-%28-2%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=2%2F2 ALIGN=MIDDLE  ALT=\"x=2%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=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can find the y coordinate by letting x=1 and solving for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%29%5E2-2%281%29-15 ALIGN=MIDDLE  ALT=\"y=%281%29%5E2-2%281%29-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-2-15 ALIGN=MIDDLE  ALT=\"y=1-2-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16 ALIGN=MIDDLE  ALT=\"y=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is (1,-16)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can find the x-intercepts, if there are any, by letting y=0 and solve for x.  This time you can factor, sometimes you have to use the quadratic formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-2x-15 ALIGN=MIDDLE  ALT=\"0=x%5E2-2x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "0=(x-5)(x+3)<BR>\n" );
document.write( "x-5=0 and x+3=0<BR>\n" );
document.write( "x-5+5=0+5  and x+3-3=0-3<BR>\n" );
document.write( "x=5 and x=-3<BR>\n" );
document.write( "The x intercepts are (-3,0) and (5,0)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can find the y-intercept by letting x=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280%29%5E2-2%280%29-15 ALIGN=MIDDLE  ALT=\"y=%280%29%5E2-2%280%29-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0-0-15 ALIGN=MIDDLE  ALT=\"y=0-0-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-15 ALIGN=MIDDLE  ALT=\"y=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercept is (0,-15)<BR>\n" );
document.write( "The graph looks 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-20%2C5%2Cx%5E2-2x-15%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-20%2C5%2Cx%5E2-2x-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );