document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142145>Question 142145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you graph the equation: y= -X^2-4X+5. If you can, please explan how u got the vertex and how to graph everything. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103496 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=103496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2-4x%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2-4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "First of all, let's find where the function intercepts the x-axis by setting f(x)=0.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-x%5E2-4x%2B5 ALIGN=MIDDLE  ALT=\"0=-x%5E2-4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <-- Make it a little easier by multiplying both sides by -1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---Factor-thought step: what numbers multiply to get -5 and add to get 4?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x%2B5%29%28x-1%29 ALIGN=MIDDLE  ALT=\"0=%28x%2B5%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <--- 5 and -1!<BR>\n" );
document.write( "Now, when can this equation be true? That is, if it equals 0, one of either term (x+5) or (x-1) must be 0. So we set each equal to zero.\r<BR>\n" );
document.write( "\n" );
document.write( "x+5=0 or x-1=0<BR>\n" );
document.write( "which means x=-5 or x=1. So we now have the x-intercepts. \r<BR>\n" );
document.write( "\n" );
document.write( "Next, the vertex of a parabola is -b/2a, when the function is in form ax^2+bx+c. So, for our purposes the vertex is x=-(-4)/2(-1)=4/(-2)=-2. The function is valued at f(-2)=-(-2)^2-4(-2)+5=-4+8+5=9. So the vertex is (-2,9). Note the direction in which the function opens: the leading coefficient is -1 (of x^2). This means it opens downward.\r<BR>\n" );
document.write( "\n" );
document.write( "Now you can graph it properly. Look at my graph below and see if you can reproduce it yourself.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-8%2C+4%2C+-4%2C+13%2C+-x%5E2-4x%2B5+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-8%2C+4%2C+-4%2C+13%2C+-x%5E2-4x%2B5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );