document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549053>Question 549053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My daughter failed her Algebra II test, and can't seem to solve these problems. <BR>\n" );
document.write( "Any help, is greatly appreciated!\r<BR>\n" );
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document.write( "Solve.<BR>\n" );
document.write( "(p + 6)2 = 17\r<BR>\n" );
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document.write( "Solve.<BR>\n" );
document.write( "6r2 + 24r = - 20\r<BR>\n" );
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document.write( "Determine whether there is a maximum or minimum value for the given function, and find that value.<BR>\n" );
document.write( "f(x) = x2 - 12x + 39\r<BR>\n" );
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document.write( "A ball is thrown downward from a window in a tall building. Its position at time t in seconds is  where s is in feet. How long (to the nearest tenth) will it take the ball to fall.\r<BR>\n" );
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document.write( "Factor:<BR>\n" );
document.write( "f(x) = x2 + 2x - 120 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357443 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve.<BR>\n" );
document.write( "(p + 6)2 = 17<BR>\n" );
document.write( "I think the 2 is an exponent.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p+%2B+6%29%5E2+=+17 ALIGN=MIDDLE  ALT=\"%28p+%2B+6%29%5E2+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+%2B+6+=+sqrt%2817%29 ALIGN=MIDDLE  ALT=\"p+%2B+6+=+sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p = -6 ± sqrt(17)<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Solve.<BR>\n" );
document.write( "6r2 + 24r = - 20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6r%5E2+%2B+24r+%2B+20+=+0 ALIGN=MIDDLE  ALT=\"6r%5E2+%2B+24r+%2B+20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B24x%2B20+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B24x%2B20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2824%29%5E2-4%2A6%2A20=96 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2824%29%5E2-4%2A6%2A20=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=96 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-24%2B-sqrt%28+96+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-24%2B-sqrt%28+96+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+96+%29%29%2F2%5C6+=+-1.18350341907227 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+96+%29%29%2F2%5C6+=+-1.18350341907227\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2824%29-sqrt%28+96+%29%29%2F2%5C6+=+-2.81649658092773 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2824%29-sqrt%28+96+%29%29%2F2%5C6+=+-2.81649658092773\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B24x%2B20 ALIGN=MIDDLE  ALT=\"6x%5E2%2B24x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B24x%2B20+=+%28x--1.18350341907227%29%2A%28x--2.81649658092773%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B24x%2B20+=+%28x--1.18350341907227%29%2A%28x--2.81649658092773%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.18350341907227, -2.81649658092773.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B24%2Ax%2B20+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B24%2Ax%2B20+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "--------<BR>\n" );
document.write( "r = -2 ± sqrt(6)/3<BR>\n" );
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document.write( "Determine whether there is a maximum or minimum value for the given function, and find that value.<BR>\n" );
document.write( "f(x) = x2 - 12x + 39 <BR>\n" );
document.write( "The coefficient of the x^2 term is +, so it's a minimum.<BR>\n" );
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document.write( "Line of Symmetry is x = -b/2a<BR>\n" );
document.write( "x = 12/2 = 6<BR>\n" );
document.write( "f(6) = 6^2 - 12*6 + 39 = 3<BR>\n" );
document.write( "Minimum at (6,3)<BR>\n" );
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document.write( "A ball is thrown downward from a window in a tall building. Its position at time t in seconds is where s is in feet. How long (to the nearest tenth) will it take the ball to fall.<BR>\n" );
document.write( "No numbers given.<BR>\n" );
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document.write( "Factor:<BR>\n" );
document.write( "f(x) = x2 + 2x - 120<BR>\n" );
document.write( "= (x-10)*(x+12) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );