document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009400>Question 1009400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground and reaches an altitude of 500 feet. If the origin represents the tee and is the ball travels along a parabolic path over the positive x-axis, find an equation for the path of the golf ball. \r<BR>\n" );
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document.write( "If the equation that fits this is: <BR>\n" );
document.write( "(x-h)^2 = 4x(y-k) \r<BR>\n" );
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document.write( "What are <BR>\n" );
document.write( "h = <BR>\n" );
document.write( "k = <BR>\n" );
document.write( "c = \r<BR>\n" );
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document.write( "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 #624889 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=624889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A simple sketch and reference to STANDARD FORM instead of the format that you show, will allow you to identify the vertex, a maximum point, and the zeros of the equation.  You can then find the factor \"a\", again in reference to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Assuming that discussion makes sense for you,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=a%28x-100%29%5E2%2B500%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=a%28x-100%29%5E2%2B500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Vertex is  (100, 500).<BR>\n" );
document.write( "Zeros are x at 0 and at 200.\r<BR>\n" );
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document.write( "What about the factor a ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-100%29%5E2=y-500 ALIGN=MIDDLE  ALT=\"a%28x-100%29%5E2=y-500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28y-500%29%2F%28x-100%29%5E2 ALIGN=MIDDLE  ALT=\"a=%28y-500%29%2F%28x-100%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use coordinates of either of the zeros....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%280-500%29%2F%28200-100%29%5E2 ALIGN=MIDDLE  ALT=\"a=%280-500%29%2F%28200-100%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-500%2F10000 ALIGN=MIDDLE  ALT=\"a=-500%2F10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-5%2F100 ALIGN=MIDDLE  ALT=\"a=-5%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or simpler<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F20 ALIGN=MIDDLE  ALT=\"a=-1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The resulting STANDARD FORM equation is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%281%2F20%29%28x-100%29%5E2%2B500%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%281%2F20%29%28x-100%29%5E2%2B500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The factor of 4 shown in the model you give, does not seem correct.  In fact, the factor shown there,  \"4x\", does not fit a quadratic equation, nor parabola.\r<BR>\n" );
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document.write( "ANSWERS FROM THIS:<BR>\n" );
document.write( "h=100<BR>\n" );
document.write( "k=500<BR>\n" );
document.write( "What is c supposed to be? What is this supposed to mean?\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "If you meant to write the form,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2=4p%28y-k%29 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2=4p%28y-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the typical result when deriving the equation of a parabola using a given vertex  (h,k) and directrix  p units from the vertex and focus p units from the vertex but on the other side from the vertex.  If your book does not have this derivation, then you can find a video showing it:  <a  rel=nofollow HREF=\"https://www.youtube.com/watch?v=Wworlx39KfQ\">vertex of parabola not at origin - derivation of equation using focus and directrix</a> </SPAN>\n" );
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