document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750622>Question 750622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there I need to calculate out how far and high a boy named Jose throws in a ball in a football match, Y stands for the height in meters and X for the diatance in meters from where jose is standing.<BR>\n" );
document.write( "How do I calculate Y=-0,04x^2+0,6x+2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456739 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=456739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Y=-0.04x^2+0.6x+2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Maximum is at vertex:<BR>\n" );
document.write( "x-value of vertex is \"axis of symmetry\":<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -0.6/(2*(-0.04))<BR>\n" );
document.write( "x = -0.6/(-0.08)<BR>\n" );
document.write( "x = 0.6/(0.08)<BR>\n" );
document.write( "x = 7.5 <BR>\n" );
document.write( "Max height:<BR>\n" );
document.write( "Y=-0.04(7.5)^2+0.6(7.5)+2<BR>\n" );
document.write( "Y= 4.25 meters (max height)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Max distance, we set Y to zero and solve for x:<BR>\n" );
document.write( "0=-0.04x^2+0.6x+2<BR>\n" );
document.write( "0=0.04x^2-0.6x-2<BR>\n" );
document.write( "0=0.02x^2-0.3x-1<BR>\n" );
document.write( "applying the \"quadratic formula\" yields:<BR>\n" );
document.write( "x = {17.81, -2.81}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving<BR>\n" );
document.write( "x = 17.81 meters (max distance)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of \"quadratic formula\":<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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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=0.02x%5E2%2B-0.3x%2B-1+=+0 ALIGN=MIDDLE  ALT=\"0.02x%5E2%2B-0.3x%2B-1+=+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=%28-0.3%29%5E2-4%2A0.02%2A-1=0.17 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-0.3%29%5E2-4%2A0.02%2A-1=0.17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0.17 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--0.3%2B-sqrt%28+0.17+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--0.3%2B-sqrt%28+0.17+%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-%28-0.3%29%2Bsqrt%28+0.17+%29%29%2F2%5C0.02+=+17.8077640640442 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-0.3%29%2Bsqrt%28+0.17+%29%29%2F2%5C0.02+=+17.8077640640442\"   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-%28-0.3%29-sqrt%28+0.17+%29%29%2F2%5C0.02+=+-2.80776406404415 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-0.3%29-sqrt%28+0.17+%29%29%2F2%5C0.02+=+-2.80776406404415\"   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=0.02x%5E2%2B-0.3x%2B-1 ALIGN=MIDDLE  ALT=\"0.02x%5E2%2B-0.3x%2B-1\"   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=0.02x%5E2%2B-0.3x%2B-1+=+0.02%28x-17.8077640640442%29%2A%28x--2.80776406404415%29 ALIGN=MIDDLE  ALT=\"0.02x%5E2%2B-0.3x%2B-1+=+0.02%28x-17.8077640640442%29%2A%28x--2.80776406404415%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 17.8077640640442, -2.80776406404415.\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+0.02%2Ax%5E2%2B-0.3%2Ax%2B-1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.02%2Ax%5E2%2B-0.3%2Ax%2B-1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );