document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194535>Question 1194535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mario is going to fly through this scene, following the path of the quadratic function 𝑓(𝑥). Based on the<BR>\n" );
document.write( "table and graph, you will write equations for this quadratic function in each of three forms: standard<BR>\n" );
document.write( "form, vertex form, and factored form. You may start with any form you choose, but you need to write<BR>\n" );
document.write( "equivalent equations in all three forms.<BR>\n" );
document.write( "equivalent equations in all three forms.<BR>\n" );
document.write( "𝑥 𝑓(𝑥)<BR>\n" );
document.write( "0 3<BR>\n" );
document.write( "1 1.25<BR>\n" );
document.write( "2 0<BR>\n" );
document.write( "3 -0.75<BR>\n" );
document.write( "4 -1<BR>\n" );
document.write( "5 -0.75<BR>\n" );
document.write( "6 0<BR>\n" );
document.write( "7 1.25<BR>\n" );
document.write( "8 3<BR>\n" );
document.write( "1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826750 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The two zeros are given as x=2 and x=6.<br><BR>\n" );
document.write( "You could start with that, knowing that the equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-2%29%28x-6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-2%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then determine the value of a using any of the given points.  e.g.,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=a%28-2%29%28-6%29=12a=3 ALIGN=MIDDLE  ALT=\"f%280%29=a%28-2%29%28-6%29=12a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F4 ALIGN=MIDDLE  ALT=\"a=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then one form of the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2F4%29%28x-2%29%28x-6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2F4%29%28x-2%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Reformat it into any form you want.<br><BR>\n" );
document.write( "Alternatively, with the zeros at x=2 and x=6, you know the axis of symmetry is x=4; and since f(4)=-1, you know the vertex is (4,-1).  Then you could start with vertex form,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-4%29%5E2-1 ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-4%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Again determine the value of a by using any of the given data points (except (4,-1))<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=a%28-4%29%5E2-1+=+16a-1+=+3 ALIGN=MIDDLE  ALT=\"f%280%29=a%28-4%29%5E2-1+=+16a-1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a=4 ALIGN=MIDDLE  ALT=\"16a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F4 ALIGN=MIDDLE  ALT=\"a=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2F4%29%28x-4%29%5E2-1 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2F4%29%28x-4%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Again reformat that in any way you need to.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );