document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157251>Question 157251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am given the zeros (ie. cross x axis at -3 and 4), and told the equation crosses the y axis at 48, how would I make a quadratic equation out of this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115896 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=115896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     I am given the zeros (ie. cross x axis at -3 and 4), and told the equation crosses the y axis at 48, how would I make a quadratic equation out of this?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the problem states that the quadratic crosses the x-axis at -3 and 4 we now KNOW two factors of the quadratic.  So far, then, we have:<BR>\n" );
document.write( "y = (x+3)(x-4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that to determine where a quadratic crosses the y-axis, set x=0 and solve for y:<BR>\n" );
document.write( "y = (x+3)(x-4)<BR>\n" );
document.write( "y = (0+3)(0-4)<BR>\n" );
document.write( "y = (3)(-4)<BR>\n" );
document.write( "y = -12<BR>\n" );
document.write( "And, because the problem states that it \"crosses the y axis at 48\"...<BR>\n" );
document.write( "To get it to 48, we ask ourself what do we multiply -12 with to get 48?  And, the answer is -4.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So, now we have:<BR>\n" );
document.write( "y=-4(x+3)(x-4)<BR>\n" );
document.write( "y=-4(x^2-x-12)<BR>\n" );
document.write( "y=-4x^2+4x+48  (this is what they are looking for)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Here's the quadratic solution:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B4x%2B48+=+0 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B4x%2B48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%284%29%5E2-4%2A-4%2A48=784 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A-4%2A48=784\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=784 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-4%2B-sqrt%28+784+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+784+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%284%29%2Bsqrt%28+784+%29%29%2F2%5C-4+=+-3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+784+%29%29%2F2%5C-4+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%284%29-sqrt%28+784+%29%29%2F2%5C-4+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%284%29-sqrt%28+784+%29%29%2F2%5C-4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B4x%2B48 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B4x%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B4x%2B48+=+-4%28x--3%29%2A%28x-4%29 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B4x%2B48+=+-4%28x--3%29%2A%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -3, 4.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B4%2Ax%2B48+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B4%2Ax%2B48+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );