document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=770382>Question 770382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! Please anybody just help me with my works. Thank you very much in advance for any of your help.\r<BR>\n" );
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document.write( "(a) Use the quadratic formula to solve the equation <BR>\n" );
document.write( "3p2 + 5p — 11 = 0.<BR>\n" );
document.write( "Give your answers correct to two decimal places.<BR>\n" );
document.write( "MY ANSWER: 1.25   and    -2.92  are these correct?\r<BR>\n" );
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document.write( "(b) Find the discriminant of the quadratic expression 7x2 — 3x — 11.<BR>\n" );
document.write( "MY ANSWER:   d=317    is it correct?\r<BR>\n" );
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document.write( "(c)  Write the quadratic expression x2 — 34x + 9 in completed-square<BR>\n" );
document.write( "form.<BR>\n" );
document.write( "MY ANSWER: (x-7)^2=280   is it correct?\r<BR>\n" );
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document.write( "(d)  Use the completed-square form from part (c) to solve the equation x2 — 34x + 9 = 0, leaving your answer in exact (surd)form.<BR>\n" );
document.write( "MY ANSWER: x1=7+2surd70    and x2=7-2surd70  are these correct?\r<BR>\n" );
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document.write( "(e)  Use the completed-square form from part (d) to write down the<BR>\n" );
document.write( "vertex of the parabola y = x2 — 34x + 9<BR>\n" );
document.write( "MY ANSWER: y=-280   x=7  are these correct?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #469484 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=469484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) Use the quadratic formula to solve the equation <BR>\n" );
document.write( "3p2 + 5p — 11 = 0.<BR>\n" );
document.write( "Give your answers correct to two decimal places.<BR>\n" );
document.write( "MY ANSWER: 1.25   and    -2.92  are these correct?<BR>\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=3x%5E2%2B5x%2B-11+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B5x%2B-11+=+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=%285%29%5E2-4%2A3%2A-11=157 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A3%2A-11=157\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=157 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+=+%28-5%2B-sqrt%28+157+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+157+%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-%285%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+1.25499401435694 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+1.25499401435694\"   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-%285%29-sqrt%28+157+%29%29%2F2%5C3+=+-2.92166068102361 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%285%29-sqrt%28+157+%29%29%2F2%5C3+=+-2.92166068102361\"   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=3x%5E2%2B5x%2B-11 ALIGN=MIDDLE  ALT=\"3x%5E2%2B5x%2B-11\"   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=3x%5E2%2B5x%2B-11+=+%28x-1.25499401435694%29%2A%28x--2.92166068102361%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B5x%2B-11+=+%28x-1.25499401435694%29%2A%28x--2.92166068102361%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.25499401435694, -2.92166068102361.\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+3%2Ax%5E2%2B5%2Ax%2B-11+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B5%2Ax%2B-11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "It's correct to 2 places.<BR>\n" );
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document.write( "(b) Find the discriminant of the quadratic expression 7x2 — 3x — 11.<BR>\n" );
document.write( "MY ANSWER:   d=317    is it correct?<BR>\n" );
document.write( "Disc = b^2 - 4ac = 9 + 4*(7*11) = 317<BR>\n" );
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document.write( "(c)  Write the quadratic expression x2 — 34x + 9 in completed-square<BR>\n" );
document.write( "form.<BR>\n" );
document.write( "MY ANSWER: (x-7)^2=280   is it correct?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+34x+%2B+9+=+%28x+-+17%29%5E2+%2B+280 ALIGN=MIDDLE  ALT=\"x%5E2+-+34x+%2B+9+=+%28x+-+17%29%5E2+%2B+280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Not (x-7)^2<BR>\n" );
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document.write( "(d)  Use the completed-square form from part (c) to solve the equation x2 — 34x + 9 = 0, leaving your answer in exact (surd)form.<BR>\n" );
document.write( "MY ANSWER: x1=7+2surd70    and x2=7-2surd70  are these correct?<BR>\n" );
document.write( "Use sqrt, not surd<BR>\n" );
document.write( "Use ^ for exponents, Shift 6<BR>\n" );
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document.write( " x^2 - 34x + 9 = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+34x+=+-9 ALIGN=MIDDLE  ALT=\"+x%5E2+-+34x+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+34x+%2B+289+=+-9+%2B+289+=+280 ALIGN=MIDDLE  ALT=\"x%5E2+-+34x+%2B+289+=+-9+%2B+289+=+280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+17%29%5E2+=+280 ALIGN=MIDDLE  ALT=\"%28x+-+17%29%5E2+=+280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-17+=+sqrt%28280%29 ALIGN=MIDDLE  ALT=\"x-17+=+sqrt%28280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-17+=+-sqrt%28280%29 ALIGN=MIDDLE  ALT=\"x+-17+=+-sqrt%28280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(e)  Use the completed-square form from part (d) to write down the<BR>\n" );
document.write( "vertex of the parabola y = x2 — 34x + 9<BR>\n" );
document.write( "MY ANSWER: y=-280   x=7  are these correct?<BR>\n" );
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