document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=786276>Question 786276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there tutors, I have a question that I don't know how to do. This is the equation : 5(x-3)^2+8.<BR>\n" );
document.write( "I have to find:<BR>\n" );
document.write( "1. The maximum or minium point.<BR>\n" );
document.write( "2. The equation of the line of symmetry or the equation of the axis of symmetry.<BR>\n" );
document.write( "3. The value of x at which the maximum or minimum of the axis of symmetry.<BR>\n" );
document.write( "4. The x co-ordinate of the minimum or maximum point.<BR>\n" );
document.write( "5. The range of the function<BR>\n" );
document.write( "6. The maximum or minimum value.<BR>\n" );
document.write( "7. The y co-ordinate of the maximum or minimum point. <BR>\n" );
document.write( "Sorry if it seems like to much and thanks to whomsoever in advance.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477856 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=477856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5%28x-3%29%5E2%2B8 ALIGN=MIDDLE  ALT=\"y+=+5%28x-3%29%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+5%28x-3%29%5E2%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29+=+5%28x-3%29%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "takes the value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <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;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For all other values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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%3C%3E0 ALIGN=MIDDLE  ALT=\"x-3%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%3E0%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x-3%29%5E2%3E0%29 ALIGN=MIDDLE  ALT=\"5%28x-3%29%5E2%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5%28x-3%29%5E2%2B8%3E8 ALIGN=MIDDLE  ALT=\"y+=+5%28x-3%29%5E2%2B8%3E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the point (3,8) (with <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a minimum, because the function's value is greater everywhere else, and it takes the value y=8 only for x=3.<BR>\n" );
document.write( " <BR>\n" );
document.write( "2) In the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > appears only in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=%28abs%28x-3%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=%28abs%28x-3%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-3%29 ALIGN=MIDDLE  ALT=\"abs%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the horizontal distance to the vertical line <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( "The value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-3%29 ALIGN=MIDDLE  ALT=\"abs%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > determines the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so that any two points on opposite sides, but at the same horizontal distance from <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;\" > have the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If the line <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;\" > were a mirror, the points of the graph on one side would be the mirror image of the points on the other side.<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;\" > is the equation of the \"line of symmetry\" or \"axis of symmetry.\"<BR>\n" );
document.write( " <BR>\n" );
document.write( "3) I do not know what you meant by \"The value of x at which the maximum or minimum of the axis of symmetry.\"<BR>\n" );
document.write( " <BR>\n" );
document.write( "4) The x co-ordinate of the minimum or maximum point is <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;\" > as explained in 1).<BR>\n" );
document.write( " <BR>\n" );
document.write( "5. The range of the function is [8,infinity) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > can get as large as you want. There are no bounds for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, except tha it must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It cannot be less than 8, but it can be more than any number you can name.\r<BR>\n" );
document.write( "\n" );
document.write( "6. The maximum or minimum value. As said for 1) the minimum value for y is 8.<BR>\n" );
document.write( " <BR>\n" );
document.write( "7. The y co-ordinate of the maximum or minimum point. y=8, as said before.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-4%2C10%2C-5%2C45%2C%28x-3%29%5E2%2B8%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-4%2C10%2C-5%2C45%2C%28x-3%29%5E2%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );