document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=301224>Question 301224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!! \r<BR>\n" );
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document.write( "The height of a ball is modeled by the equation y=-1/70 x^2+2x+2 where x is the horizontal feet and y the vertical feet. \r<BR>\n" );
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document.write( "A) How high is the ball when you hit it?\r<BR>\n" );
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document.write( "B) What is the ball's maximum heigh?\r<BR>\n" );
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document.write( "C) How far from where you hit the ball does it strike the ground?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #216048 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=216048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of a ball is modeled by the equation y=-1/70 x^2+2x+2 where x is the horizontal feet and y the vertical feet. <BR>\n" );
document.write( "A) How high is the ball when you hit it?<BR>\n" );
document.write( "Assuming x is the distance from where it's hit:<BR>\n" );
document.write( "x = 0 --> y = 2<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "B) What is the ball's maximum heigh?<BR>\n" );
document.write( "It's a parabola, find the vertex:<BR>\n" );
document.write( "@ x = -b/2a = -2/(-1/35) = 70<BR>\n" );
document.write( "y = -(1/70)*70^2 + 140 + 2<BR>\n" );
document.write( "y = 72<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "C) How far from where you hit the ball does it strike the ground? <BR>\n" );
document.write( "At y = 0<BR>\n" );
document.write( "-x^2/70 + 2x + 2 = 0<BR>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=-0.0142857142857143x%5E2%2B2x%2B2+=+0 ALIGN=MIDDLE  ALT=\"-0.0142857142857143x%5E2%2B2x%2B2+=+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=%282%29%5E2-4%2A-0.0142857142857143%2A2=4.11428571428571 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A-0.0142857142857143%2A2=4.11428571428571\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4.11428571428571 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+=+%28-2%2B-sqrt%28+4.11428571428571+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+4.11428571428571+%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-%282%29%2Bsqrt%28+4.11428571428571+%29%29%2F2%5C-0.0142857142857143+=+-0.992957397195394 ALIGN=MIDDLE   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-%282%29-sqrt%28+4.11428571428571+%29%29%2F2%5C-0.0142857142857143+=+140.992957397195 ALIGN=MIDDLE   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=-0.0142857142857143x%5E2%2B2x%2B2 ALIGN=MIDDLE  ALT=\"-0.0142857142857143x%5E2%2B2x%2B2\"   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=-0.0142857142857143x%5E2%2B2x%2B2+=+%28x--0.992957397195394%29%2A%28x-140.992957397195%29 ALIGN=MIDDLE  ALT=\"-0.0142857142857143x%5E2%2B2x%2B2+=+%28x--0.992957397195394%29%2A%28x-140.992957397195%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.992957397195394, 140.992957397195.\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+-0.0142857142857143%2Ax%5E2%2B2%2Ax%2B2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.0142857142857143%2Ax%5E2%2B2%2Ax%2B2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "=~ 140.993 feet </SPAN>\n" );
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