document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425905>Question 425905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find the vertx, value of p, axis of symmetry, focus, and directrix of each porabola, and then graph.<BR>\n" );
document.write( "y= 1/32(x+)^2<BR>\n" );
document.write( "hOW TO write  the eqauation in standrard for for each porabola  <BR>\n" );
document.write( "a. vertex (0,0), focus(0,1)<BR>\n" );
document.write( "b. vertex(0,0), focus (-8,0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296405 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=296405\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to find the vertx, value of p, axis of symmetry, focus, and directrix of each parabola, and then graph.<BR>\n" );
document.write( "y= (1/32)x^2<BR>\n" );
document.write( "hOW TO write the equation in standard for for each porabola<BR>\n" );
document.write( "a. vertex (0,0), focus(0,1)<BR>\n" );
document.write( "b. vertex(0,0), focus (-8,0)\r<BR>\n" );
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document.write( "..\r<BR>\n" );
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document.write( "y=1/32(x^2<BR>\n" );
document.write( "This of the form, (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex. Since you don't see h or k in the equation, the vertex must be at the origin, (0,0).<BR>\n" );
document.write( "rewriting given equation,<BR>\n" );
document.write( "x^2=32y<BR>\n" );
document.write( "This is a parabola that opens upwards with its vertex at the (0,0), and axis of symmetry,x=0 or the y-axis.<BR>\n" );
document.write( "4p=32<BR>\n" );
document.write( "p=8<BR>\n" );
document.write( "The focus on the axis of symmetry is 8 units above the center at (0,8).<BR>\n" );
document.write( "The directrix is a line, y=-8<BR>\n" );
document.write( "See the graph of this parabola below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F32%29x%5E2%2C-8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F32%29x%5E2%2C-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "a. vertex (0,0), focus(0,1)<BR>\n" );
document.write( "From the focal point (0,1), it can be seen that the axis of symmetry is the y-axis like the previous parabola and it opens upwards with p=1 and its directrix at y=-1<BR>\n" );
document.write( "Equation: x^2=4y<BR>\n" );
document.write( "See the graph below:(Note that the higher the coefficient of x^2, the steeper the curve, that is, a higher slope)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2F4%2C-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2F4%2C-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "b. vertex(0,0), focus (-8,0)<BR>\n" );
document.write( "Again, gleaning information from the focal point, it can be seen that the axis of symmetry is x=0 or the x-axis and it opens sideways to the left with p=8 and its directrix at x=8.<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y^2=-32x<BR>\n" );
document.write( "See the graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C%28-32x%29%5E.5%2C-%28-32x%29%5E.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C%28-32x%29%5E.5%2C-%28-32x%29%5E.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );