document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105257>Question 105257</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131808583/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> what can a and k be so both points are on the graph of function?<BR>\n" );
document.write( "points are (1,11) and (2,-19); function is y= a(x+1)^2 + k<BR>\n" );
document.write( "how can i find the function so that both poitns are on the graph?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76600 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=76600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One way to do these is to substitute the x- and y-values from the given points into the equation, thus giving you a system of equations with two unknowns (a and k). Then solve the system of equations for the two unknowns.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 1 and y = 11 from the first point (1, 11) to get the first equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+a%281%2B1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"11+=+a%281%2B1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+4a%2Bk ALIGN=MIDDLE  ALT=\"11+=+4a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute the x- and y-values from the second point (2, -19) to get the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+a%282%2B1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-19+=+a%282%2B1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+9a%2Bk ALIGN=MIDDLE  ALT=\"-19+=+9a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "So now you have the two equatios:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+4a%2Bk ALIGN=MIDDLE  ALT=\"11+=+4a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+9a%2Bk ALIGN=MIDDLE  ALT=\"-19+=+9a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > You can solve these by any of the accepted methods for solving systems of equations. Let's use elimination by subtracting equation 1) from equation 2) and solving for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30+=+5a ALIGN=MIDDLE  ALT=\"-30+=+5a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-6 ALIGN=MIDDLE  ALT=\"a+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitute this value of a into either equation 1) or equation 2) and solve for k. Let's use equation 1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+4a%2Bk ALIGN=MIDDLE  ALT=\"11+=+4a%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute a = -6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+4%28-6%29%2Bk ALIGN=MIDDLE  ALT=\"11+=+4%28-6%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+-24%2Bk ALIGN=MIDDLE  ALT=\"11+=+-24%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 24 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+35 ALIGN=MIDDLE  ALT=\"k+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check: Into the original equation, substitute a = -6 and k = 35.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%28x%2B1%29%5E2%2B35 ALIGN=MIDDLE  ALT=\"y+=+-6%28x%2B1%29%5E2%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's see if the two given points (1, 11) and (2, -19) satisfy this equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+-6%281%2B1%29%5E2%2B35 ALIGN=MIDDLE  ALT=\"11+=+-6%281%2B1%29%5E2%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+-6%284%29%2B35 ALIGN=MIDDLE  ALT=\"11+=+-6%284%29%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+-24%2B35 ALIGN=MIDDLE  ALT=\"11+=+-24%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+11 ALIGN=MIDDLE  ALT=\"11+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Ok for the first point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+-6%282%2B1%29%5E2%2B35 ALIGN=MIDDLE  ALT=\"-19+=+-6%282%2B1%29%5E2%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+-6%289%29%2B35 ALIGN=MIDDLE  ALT=\"-19+=+-6%289%29%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+-54%2B35 ALIGN=MIDDLE  ALT=\"-19+=+-54%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19+=+-19 ALIGN=MIDDLE  ALT=\"-19+=+-19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Ok for the second point. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );