document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137128>Question 137128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I compute the x and y axis intercepts of a quadratic function? Please provide an example to illustrate  the explanation. 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 #100334 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=100334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can find the x- and y-intercepts of a quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >as follows:<BR>\n" );
document.write( "1) Set x = 0 and solve for y. This will give you the y-intercept.<BR>\n" );
document.write( "2) Set y = 0 and solve for x. This will give you the x-intercept.<BR>\n" );
document.write( "Here's an example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2-8x%2B12 ALIGN=MIDDLE  ALT=\"y+=+x%5E2-8x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Find the x- and y-intercepts. <BR>\n" );
document.write( "1) Set x = 0 and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280%29%5E2-8%280%29%2B12 ALIGN=MIDDLE  ALT=\"y+=+%280%29%5E2-8%280%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+12 ALIGN=MIDDLE  ALT=\"y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > The y-intercept is: (0, 12)<BR>\n" );
document.write( "2) Set y = 0 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2-8x%2B12 ALIGN=MIDDLE  ALT=\"0+=+x%5E2-8x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the trinomial:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > from which we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > These are the x-intercepts. These are also called the \"zeros\" or the \"roots\" of the equation and notice that they are \"real\" numbers, which really means that the equation has real x-intercepts.<BR>\n" );
document.write( "Of course, not all quadratic equations will have x-intercepts but they will alway have a y-intercept.<BR>\n" );
document.write( "Here's a graph of the given example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C8%2C-5%2C15%2Cx%5E2-8x%2B12%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C8%2C-5%2C15%2Cx%5E2-8x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's an example in which the quadratic equation has no x-intercepts.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1) Set x = 0 and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%280%29%5E2%2B4%280%29%2B5 ALIGN=MIDDLE  ALT=\"y+=+%280%29%5E2%2B4%280%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5 ALIGN=MIDDLE  ALT=\"y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the y-intercept.<BR>\n" );
document.write( "2) Set y = 0 and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"0+=+x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the quadratic formula to solve: (You can do the details)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2Bi ALIGN=MIDDLE  ALT=\"x+=+-2%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2-i ALIGN=MIDDLE  ALT=\"x+=+-2-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > No \"real\" roots so no x-intercepts.<BR>\n" );
document.write( "Here's the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C8%2Cx%5E2%2B4x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C8%2Cx%5E2%2B4x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );