document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=802814>Question 802814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An engineer is designing a parabolic arch. The arch must be 15m high and 6m wide at a height of 8m. Determine a quadratic function that satisfies these conditions and the width of the arch at its base.\r<BR>\n" );
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document.write( "This is what I have so far:\r<BR>\n" );
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document.write( "vertex (x,15)<BR>\n" );
document.write( "passes through point (6,8)\r<BR>\n" );
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document.write( "h(w)= a(x-h)^2+15\r<BR>\n" );
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document.write( "Can you help me with the rest.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484023 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=484023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it passes through point (6,8), it would need to pass through (0,8); the vertex will be at (3,15), and the base will be from a point (-b,0), to a point (6+b,0).<BR>\n" );
document.write( "That makes it complicated.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Let's put the origin (0,0) at a point on the ground, directly below the vertex.<BR>\n" );
document.write( "We make the line that passes through the feet of the arch the x-axis.<BR>\n" );
document.write( "We call the vertical axis of symmetry of the arch our y-axis.<BR>\n" );
document.write( "We measure x (the horizontal distance to the origin) in meters,<BR>\n" );
document.write( "and y or h(x) (the height above the ground) also in meters.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=ax%5E2%2B15 ALIGN=MIDDLE  ALT=\"h%28x%29=ax%5E2%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our equation<BR>\n" );
document.write( "The vertex will be (0,15).<BR>\n" );
document.write( "The points at a height of 8 meters will be (-3,8) and (3,8), so that the arch width at that height is the (horizontal distance from (-3,8) to 3,8, which is 6.<BR>\n" );
document.write( "Substituting the coordinates of (3,8), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=+a%2A3%5E3%2B15 ALIGN=MIDDLE  ALT=\"8=+a%2A3%5E3%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=9a%2B15 ALIGN=MIDDLE  ALT=\"8=9a%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-15=9a ALIGN=MIDDLE  ALT=\"8-15=9a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a=-7 ALIGN=MIDDLE  ALT=\"9a=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-7%2F9 ALIGN=MIDDLE  ALT=\"a=-7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h%28x%29=%28-7%2F9%29x%5E2%2B15%29 ALIGN=MIDDLE  ALT=\"highlight%28h%28x%29=%28-7%2F9%29x%5E2%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At the base, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=0 ALIGN=MIDDLE  ALT=\"h%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%2F9%29x%5E2%2B15=0 ALIGN=MIDDLE  ALT=\"%28-7%2F9%29x%5E2%2B15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > needs to be solved<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%2F7%29%28-7%2F9%29x%5E2=-15%28-9%2F7%29 ALIGN=MIDDLE  ALT=\"%28-9%2F7%29%28-7%2F9%29x%5E2=-15%28-9%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=15%2A9%2F7 ALIGN=MIDDLE  ALT=\"x%5E2=15%2A9%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=135%2F7 ALIGN=MIDDLE  ALT=\"x%5E2=135%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The feet of the arch are at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%28135%2F7%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%28135%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28135%2F7%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28135%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the width at the base is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28135%2F7%29-%28-sqrt%28135%2F7%29%29=2sqrt%28135%2F7%29 ALIGN=MIDDLE  ALT=\"sqrt%28135%2F7%29-%28-sqrt%28135%2F7%29%29=2sqrt%28135%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approx. 7.75 meters<BR>\n" );
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