document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35931>Question 35931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, We included the table of numbers that we have chosen. Any help, especially with graphing the answer would be highly appreciated. Thank you.\r<BR>\n" );
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document.write( "When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminate is b2 - 4ac. This discriminate can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )<BR>\n" );
document.write( "•	Explain what the value of the discriminate means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminate.  Then, graph the corresponding equation. <BR>\n" );
document.write( "DISCRIMINATE: b^2-4ac\r<BR>\n" );
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document.write( "                     A	                       B	                       C	Discriminate<BR>\n" );
document.write( "b^2-4ac<BR>\n" );
document.write( "2	6	4	4<BR>\n" );
document.write( "9	6	3	144<BR>\n" );
document.write( " 1	5	3	13<BR>\n" );
document.write( "4	10	7	-12  {-3.4} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22510 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING AND TRY<BR>\n" );
document.write( "When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )<BR>\n" );
document.write( "Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.<BR>\n" );
document.write( "CASE 1....DISCRIMINANT (D SAY) IS POSITIVE.....<BR>\n" );
document.write( "EX..LET Y = X^2-5X+6=0..<BR>\n" );
document.write( "D=5^2-4*1*6=25-24=1...<BR>\n" );
document.write( "HENCE ROOTS ARE <BR>\n" );
document.write( "REAL,THAT IS THE GRAPH CUTS THE X AXIS AT 2 REAL POINTS<BR>\n" );
document.write( "DISTINCT ...2 AND 3<BR>\n" );
document.write( "AND THE FUNCTION Y COULD BE POSITIVE OR NEGATIVE WITH A MAXIMUM OR MINIMUM<BR>\n" );
document.write( "SEE GRAPH BELOW<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+-10%2C+10%2C+x%5E2-5x%2B6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-5x%2B6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "CASE 2.....D=0<BR>\n" );
document.write( "EX....LET...Y=X^2-2X+1=0<BR>\n" );
document.write( "D=2^2-4*1*1=4-4=0<BR>\n" );
document.write( "HENCE ROOTS ARE <BR>\n" );
document.write( "REAL.THAT IS THE GRAPH CUTS THE X AXIS AT 1 REAL POINT.<BR>\n" );
document.write( "EQUAL...1 AND 1 <BR>\n" );
document.write( "AND THE FUNCTION Y IS ALWAYS NON NEGATIVE OR NON POSITIVE DEPENDING ON THE SIGN OF COEFFICIENT OF X^2 BEING POSITIVE OR NEGATIVE , WITH A MINIMUM OR MAXIMUM VALUE OF ZERO.<BR>\n" );
document.write( "SEE GRAPH BELOW.<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+-10%2C+10%2C+x%5E2-2x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-2x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "CASE 3.......D IS NEGATIVE<BR>\n" );
document.write( "EX....LET Y = X^2+X+1=0<BR>\n" );
document.write( "D=1^2-4*1*1=1-4=-3<BR>\n" );
document.write( "HENCE ROOTS ARE<BR>\n" );
document.write( "IMAGINARY.THAT IS THE GRAPH DOES NOT CUT  THE X AXIS.<BR>\n" );
document.write( "DISTINCT.....(-1+iSQRT(3))/2....AND (-1-iSQRT(3))/2<BR>\n" );
document.write( "AND THE FUNCTION  Y IS ALWAYS POSITIVE SINCE COEFFICIENT OF X^2 IS POSITIVE.<BR>\n" );
document.write( "SEE THE GRAPH BELOW...<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+-10%2C+10%2C+x%5E2%2Bx%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "EX....LET Y = -X^2+X-1=0<BR>\n" );
document.write( "D=1^2-4*(-1)*(-1)=1-4=-3<BR>\n" );
document.write( "HENCE ROOTS ARE<BR>\n" );
document.write( "IMAGINARY.THAT IS THE GRAPH DOES NOT CUT THE X AXIS.<BR>\n" );
document.write( "DISTINCT.....(1-iSQRT(3))/2....AND (1+iSQRT(3))/2<BR>\n" );
document.write( "AND THE FUNCTION  Y IS ALWAYS NEGATIVE SINCE COEFFICIENT OF X^2 IS NEGATIVE.<BR>\n" );
document.write( "SEE THE GRAPH BELOW...<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+-10%2C+10%2C+-x%5E2%2Bx-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2Bx-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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