document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=399586>Question 399586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = &#8722;2x^2&#8722; 4x + 15 please do step by step so i can understand\r<BR>\n" );
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document.write( "1.Express the quadratic function in standard form. how did you get the numbers<BR>\n" );
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document.write( "2.vertex      (x, y) =  how did you get the numbers\r<BR>\n" );
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document.write( "3.x-intercepts         (x, y) =  Small value)\r<BR>\n" );
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document.write( "4.(x, y) =                larger value)\r<BR>\n" );
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document.write( "5.y-intercept      (x, y) =  \r<BR>\n" );
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document.write( "graph and where do the numbers meet???\r<BR>\n" );
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document.write( "Thank you soo much... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282965 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=282965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)= &#8722;2x^2&#8722; 4x + 15<BR>\n" );
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document.write( "y intercept, when x=0 is 15<BR>\n" );
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document.write( "x intercepts when y=0:<BR>\n" );
document.write( "x=(-2-sqrt(34))/2, x=(-2+sqrt(34))/2 See below.<BR>\n" );
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document.write( "f(x)=a(x-h)^2+k the standard form. The vertex is the point (h,k)=-2(x^2+2x)+15<BR>\n" );
document.write( "=-2(x^2+2x+1-1)+15 completing the square<BR>\n" );
document.write( "=-2(x^2+2x+1)+2+15<BR>\n" );
document.write( "=-2(x+1)^2+17 the standard form.<BR>\n" );
document.write( "a=-2, h=-1, k=17<BR>\n" );
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document.write( "(-1, 17) vertex.<BR>\n" );
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document.write( "Ed<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=quadratic.solver>SOLVE quadratic equation with variable</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=-2x%5E2%2B-4x%2B15+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-4x%2B15+=+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=%28-4%29%5E2-4%2A-2%2A15=136 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4%29%5E2-4%2A-2%2A15=136\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=136 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--4%2B-sqrt%28+136+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4%2B-sqrt%28+136+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+136+%29%29%2F2%5C-2+=+-3.91547594742265 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+136+%29%29%2F2%5C-2+=+-3.91547594742265\"   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-%28-4%29-sqrt%28+136+%29%29%2F2%5C-2+=+1.91547594742265 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+136+%29%29%2F2%5C-2+=+1.91547594742265\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B-4x%2B15 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-4x%2B15\"   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=-2x%5E2%2B-4x%2B15+=+-2%28x--3.91547594742265%29%2A%28x-1.91547594742265%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B-4x%2B15+=+-2%28x--3.91547594742265%29%2A%28x-1.91547594742265%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -3.91547594742265, 1.91547594742265.\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+-2%2Ax%5E2%2B-4%2Ax%2B15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-4%2Ax%2B15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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