document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955425>Question 955425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=x^2/16+21x/16+11/8     the equation is x^2 devided by16 + 21x devided by 16   <BR>\n" );
document.write( "                          + 11 devided by 8\r<BR>\n" );
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document.write( "s a parabola.\r<BR>\n" );
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document.write( "(i) Is the parabola u-shaped or n-shaped? How can you tell this from\r<BR>\n" );
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document.write( "the equation? [1]\r<BR>\n" );
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document.write( "(ii) Use algebra to find the x-intercepts. [4]\r<BR>\n" );
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document.write( "(iii) Explain why the y-intercept is 11/8\r<BR>\n" );
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document.write( "(iv) Find the equation of the axis of symmetry, explaining your\r<BR>\n" );
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document.write( "method. Use this information to find the coordinates of the\r<BR>\n" );
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document.write( "vertex, rounding your answers where necessary to one decima i think the parabol is u shaped due to their being a negative number in the equation. i think the 2nd answer is y=x^2/16+21x/16+11/8 16y=x^2+21x+22 \r<BR>\n" );
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document.write( "16y-x^2-21x-22=0 ax^2+bx+c=0 a=-1, b=-21, c=-22+16y\r<BR>\n" );
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document.write( "x=21 sqrt64y+353/-2 21-sqrt 64y+353/-2 simplyfy \r<BR>\n" );
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document.write( "x=21+sqrt 64y+353/2 - 21-sqrt 64y+353/2''.\r<BR>\n" );
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document.write( "       </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583701 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=583701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2F16%2B21x%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"y=x%5E2%2F16%2B21x%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "(i) Is the parabola u-shaped or n-shaped? How can you tell this from\r<BR>\n" );
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document.write( "the equation? \r<BR>\n" );
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document.write( "the parabola is u-shaped, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F16 ALIGN=MIDDLE  ALT=\"a=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "(ii) Use algebra to find the x-intercepts. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2F16%2B21x%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"y=x%5E2%2F16%2B21x%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... x-intercepts occur where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2F16%2B21x%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"0=x%5E2%2F16%2B21x%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2A16=16x%5E2%2F16%2B%2816%2A21x%29%2F16%2B%2816%2A11%29%2F8+ ALIGN=MIDDLE  ALT=\"0%2A16=16x%5E2%2F16%2B%2816%2A21x%29%2F16%2B%2816%2A11%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B21x%2B2%2A11+ ALIGN=MIDDLE  ALT=\"0=x%5E2%2B21x%2B2%2A11+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B21x%2B22+ ALIGN=MIDDLE  ALT=\"0=x%5E2%2B21x%2B22+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+%2B-+sqrt%28+21%5E2-4%2A1%2A22+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+%2B-+sqrt%28+21%5E2-4%2A1%2A22+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+%2B-+sqrt%28+441-88+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+%2B-+sqrt%28+441-88+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+%2B-+sqrt%28+353+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+%2B-+sqrt%28+353+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........exact solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+%2B-+18.79%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+%2B-+18.79%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "approximate solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+%2B+18.79%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+%2B+18.79%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-1.11 ALIGN=MIDDLE  ALT=\"x+=-1.11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-21+-+18.79%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-21+-+18.79%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-19.9 ALIGN=MIDDLE  ALT=\"x+=-19.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(iii) Explain why the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y-intercept occurs where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, yielding (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F8 ALIGN=MIDDLE  ALT=\"11%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%5E2%2F16%2B21%2A0%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"y=0%5E2%2F16%2B21%2A0%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(iv) Find the equation of the axis of symmetry, explaining your\r<BR>\n" );
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document.write( "method. Use this information to find the coordinates of the\r<BR>\n" );
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document.write( "vertex, rounding your answers where necessary to one decimal\r<BR>\n" );
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document.write( "The axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F16 ALIGN=MIDDLE  ALT=\"a=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=21%2F16 ALIGN=MIDDLE  ALT=\"b=21%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%2821%2F16%29%2F%282%281%2F16%29%29 ALIGN=MIDDLE  ALT=\"x+=+-%2821%2F16%29%2F%282%281%2F16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%2821%2Fcross%2816%29%29%2F%282%2Fcross%2816%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+-%2821%2Fcross%2816%29%29%2F%282%2Fcross%2816%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%2821%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+-%2821%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10.5 ALIGN=MIDDLE  ALT=\"x+=+-10.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " That is also x-coordinate of the vertex, plug it in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2F16%2B21x%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"y=x%5E2%2F16%2B21x%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find y-coordinate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-10.5%29%5E2%2F16%2B21%2A%28-10.5%29%2F16%2B11%2F8+ ALIGN=MIDDLE  ALT=\"y=%28-10.5%29%5E2%2F16%2B21%2A%28-10.5%29%2F16%2B11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5.5 ALIGN=MIDDLE  ALT=\"y=-5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the vertex is at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10.5 ALIGN=MIDDLE  ALT=\"-10.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5.5 ALIGN=MIDDLE  ALT=\"-5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-25%2C+10%2C+-10%2C+10%2Cline%28-10.5%2C10%2C-10.5%2C-10%29%2Ccircle%28-10.5%2C-5.5%2C.25%29%2Clocate%28-10.5%2C-5.5%2CV%28-10.5%2C-5.5%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-25%2C+10%2C+-10%2C+10%2C+x%5E2%2F16%2B21x%2F16%2B11%2F8%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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