document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211831>Question 211831</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> evaluate the discriminate b^2-4ac, then use the answer to state how many real-number solutions exist for the equation y=x^2+8x+16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160039 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is y=x^2+8x+16<BR>\n" );
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document.write( "this is in the standard form of the equation.<BR>\n" );
document.write( "you find the roots when you set y = 0 and solve.<BR>\n" );
document.write( "your equation becomes:<BR>\n" );
document.write( "x^2 + 8x + 16 = 0<BR>\n" );
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document.write( "to find the roots using the quadratic formula, you would get the coefficients and plug them into that equation.<BR>\n" );
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document.write( "standard form of a quadratic equation is:<BR>\n" );
document.write( "ax^2 + bx +  c = 0<BR>\n" );
document.write( "your equation makes:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 8<BR>\n" );
document.write( "c = 16<BR>\n" );
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document.write( "the discriminant in this equation is b^-4ac<BR>\n" );
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document.write( "if b^2-4ac = 0, then you have one real root.<BR>\n" );
document.write( "if b^2-4ac = positive you have two real roots.<BR>\n" );
document.write( "if b^2-4ac = positive and a perfect square you have two real integer roots.  This assumes that a and c are also integers.<BR>\n" );
document.write( "if b^2-4ac = negative you have two imaginary roots.<BR>\n" );
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document.write( "imaginary root means your graph does not cross the x-axis.<BR>\n" );
document.write( "it is either above it or below it but never crosses it.<BR>\n" );
document.write( "it would be above it if the x^2 portion of your equation is positive.<BR>\n" );
document.write( "it would be below it if the x^2 portion of your equation is negative.<BR>\n" );
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document.write( "b^2-4ac = (8^2 - 4*1*16) = 64 - 64 = 0<BR>\n" );
document.write( "your equation will have one root.<BR>\n" );
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document.write( "the quadratic formula says that this root will be at -8 +/- sqrt(0)/2 which makes it at -4.<BR>\n" );
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document.write( "graph of your equation is shown below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B8x%2B16%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B8x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you have one root at x = -4.<BR>\n" );
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