document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134725>Question 134725</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/061838670X/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am completely lost on how to do these. Any help would be great.<BR>\n" );
document.write( "It says:<BR>\n" );
document.write( "Sketch the graph of the following. Label vertex, x-and y-intercepts.<BR>\n" );
document.write( "f(x)=x^2-x-12\r<BR>\n" );
document.write( "\n" );
document.write( "Vertex=( , )<BR>\n" );
document.write( "x-intercepts=( , );( , )<BR>\n" );
document.write( "y-intercept=( , ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98606 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am completely lost on how to do these. Any help would be great.<BR>\n" );
document.write( "It says:<BR>\n" );
document.write( "Sketch the graph of the following. Label vertex, x-and y-intercepts.<BR>\n" );
document.write( "f(x) = x^2 - x - 12<BR>\n" );
document.write( "Here's how you can sketch a graph<BR>\n" );
document.write( "f(x) = y so we have:<BR>\n" );
document.write( "y = x^2 - x - 12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We will find the values of y by substituting -5 to +5 in the equation<BR>\n" );
document.write( "A table of these value will be:<BR>\n" );
document.write( " x | y<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "-5 |+18<BR>\n" );
document.write( "-4 |+8<BR>\n" );
document.write( "-3 |0; when y = 0, this is one of the x intercepts<BR>\n" );
document.write( "-2 |-6<BR>\n" );
document.write( "-1 |-10<BR>\n" );
document.write( " 0 |-12; notice when x = 0, the value of y is 12, this is the y intercept<BR>\n" );
document.write( "+1 |-12; it has reached a minimum and started back up again<BR>\n" );
document.write( "+2 |-10<BR>\n" );
document.write( "+3 |-6<BR>\n" );
document.write( "+4 | 0; this is the 2nd x intercept<BR>\n" );
document.write( "+5 |+8<BR>\n" );
document.write( "Plot these values, it should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-16%2C+10%2C+x%5E2-x-12%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-16%2C+10%2C+x%5E2-x-12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Vertex=( , )<BR>\n" );
document.write( "To find the vertex, first find the axis of symmetry. This can be found using the formula x = -b/(2a)<BR>\n" );
document.write( "In this equation a=1; b=-1<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-1%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"%28-%28-1%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or .5<BR>\n" );
document.write( "Find the vertex by substituting 1/2 for x in the original equation:<BR>\n" );
document.write( "y = .5^2 - .5 - 12<BR>\n" );
document.write( "y= .25 - .5 - 12<BR>\n" );
document.write( "y = -12.25<BR>\n" );
document.write( "The x/y values for the vertex is: .5, -12.25, this is the minimum as you can see by the graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x-intercepts=( , );( , <BR>\n" );
document.write( "x intercepts are the points which the graph crosses the x axis (y=0)<BR>\n" );
document.write( "you can find them by solving the equation<BR>\n" );
document.write( "x^2 - x - 12 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-4)(x+3) = 0<BR>\n" );
document.write( "x = +4<BR>\n" );
document.write( "x = -3; the x intercepts<BR>\n" );
document.write( ":<BR>\n" );
document.write( "y-intercept=( , )<BR>\n" );
document.write( "As we said the y intercept occurs when x = 0, you see when substitute 0 for x in the equation; y = -12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did this help you? Do you have any questions? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );