document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=823880>Question 823880</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need not only answers,but  detail solution too<BR>\n" );
document.write( "The points (-4,0), (-3,-6), (-2, -10) and (1,-10) lie on the curve y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Find a,<BR>\n" );
document.write( "b and c and hence draw the curve showing clearly the turning point. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #495933 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=495933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A key to a quick solution is noticing that the points (-2, -10) and (1, -10) have the same y-coordinate. Because of the symmetry of parabolas, these two points tells us that the axis of symmetry and the vertex are halfway between -2 and 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2B1%29%2F2+=+-1%2F2 ALIGN=MIDDLE  ALT=\"%28-2%2B1%29%2F2+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the x-coordinate of the vertex is -1/2.<br><BR>\n" );
document.write( "We will use this to build the vertex form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the equation of this parabola. (Then we will transform the equation into standard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > form.) In the vertex form the \"h\" and the \"k\" are the x and y coordinates of the vertex. Since we have already found the x-coordinate we can start with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-%28-1%2F2%29%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-%28-1%2F2%29%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B1%2F2%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B1%2F2%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we will substitute in the coordinates of the given points. I'll use (1, -10):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29+=+a%28%281%29%2B1%2F2%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"%28-10%29+=+a%28%281%29%2B1%2F2%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10+=+a%283%2F2%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"-10+=+a%283%2F2%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10+=+a%289%2F4%29+%2B+k ALIGN=MIDDLE  ALT=\"-10+=+a%289%2F4%29+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10+=+%289%2F4%29a+%2B+k ALIGN=MIDDLE  ALT=\"-10+=+%289%2F4%29a+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving this for k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%289%2F4%29a+-+10+=+k ALIGN=MIDDLE  ALT=\"-%289%2F4%29a+-+10+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we'll repeat this with another point. I'll use (-3, -6):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29+=+a%28%28-3%29%2B1%2F2%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"%28-6%29+=+a%28%28-3%29%2B1%2F2%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+a%28-5%2F2%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"-6+=+a%28-5%2F2%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+a%2825%2F4%29+%2B+k ALIGN=MIDDLE  ALT=\"-6+=+a%2825%2F4%29+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+%2825%2F4%29a+%2B+k ALIGN=MIDDLE  ALT=\"-6+=+%2825%2F4%29a+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we'll substitute, into this equation, the expression we got earlier for k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+%2825%2F4%29a+%2B+%28-%289%2F4%29a+-+10%29 ALIGN=MIDDLE  ALT=\"-6+=+%2825%2F4%29a+%2B+%28-%289%2F4%29a+-+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With only the \"a\" left, we can solve for it. Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+%2816%2F4%29a+-+10%29 ALIGN=MIDDLE  ALT=\"-6+=+%2816%2F4%29a+-+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+4a+-+10%29 ALIGN=MIDDLE  ALT=\"-6+=+4a+-+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 10:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+4a%29 ALIGN=MIDDLE  ALT=\"4+=+4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing by 4:<BR>\n" );
document.write( "1 = a<br><BR>\n" );
document.write( "Now we can use this to find k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%289%2F4%29a+-+10+=+k ALIGN=MIDDLE  ALT=\"-%289%2F4%29a+-+10+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%289%2F4%29%281%29+-+10+=+k ALIGN=MIDDLE  ALT=\"-%289%2F4%29%281%29+-+10+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F4+-+40%2F4+=+k ALIGN=MIDDLE  ALT=\"-9%2F4+-+40%2F4+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-49%2F4+=+k ALIGN=MIDDLE  ALT=\"-49%2F4+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Our vertex form is now complete:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%29%28x%2B1%2F2%29%5E2+%2B+%28-49%2F4%29 ALIGN=MIDDLE  ALT=\"y+=+%281%29%28x%2B1%2F2%29%5E2+%2B+%28-49%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B1%2F2%29%5E2+%2B+%28-49%2F4%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B1%2F2%29%5E2+%2B+%28-49%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With h = -1/2 and k = -49/4, the vertex/\"turning point\" is (-1/2, -49/4).<br><BR>\n" );
document.write( "All that's left is to transform this into standard form. Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%29%5E2%2B2%28x%29%281%2F2%29%2B+%281%2F2%29%5E2+%2B+%28-49%2F4%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%29%5E2%2B2%28x%29%281%2F2%29%2B+%281%2F2%29%5E2+%2B+%28-49%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2Bx%2B+1%2F4+%2B+%28-49%2F4%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2Bx%2B+1%2F4+%2B+%28-49%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2Bx%2B+%28-48%2F4%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2Bx%2B+%28-48%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2Bx%2B+%28-12%29 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2Bx%2B+%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );