document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=18723>Question 18723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could some one help me understand this problem?\r<BR>\n" );
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document.write( "The instructions are to solve the inequality. Find the vertex and intercepts, then graph it:<BR>\n" );
document.write( "y = -x^2 - 3x - 2\r<BR>\n" );
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document.write( "Thanks very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8971 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=8971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The instructions are to solve the inequality. Find the vertex and intercepts, then graph it:<BR>\n" );
document.write( "y = -x^2 - 3x - 2<BR>\n" );
document.write( "y=-(x^2+3x+2)=-(x^2+2x+x+2)=-(x(x+2)+1(x+2))=-(x+1)(x+2)<BR>\n" );
document.write( "we first analyse this ..that is what will be its value if x=0,when will y be zero ,when is it positive,when is it -ve,has it got a maximum or minimum etc...<BR>\n" );
document.write( "we can give different values for x and find the corresponding values of y to graph it..let us do <BR>\n" );
document.write( "let us put x=0....1....2....3....-1....-2....-3....to show you the method<BR>\n" );
document.write( "we get.....y=-2...-6...-12..-20...0.....0....-2....etc..now you can plot a graph with this table...you can take more points also and do it.. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+150%2C+100%2C+-6%2C+6%2C-60%2C5%2C-x%5E2-3x-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+150%2C+100%2C+-6%2C+6%2C-60%2C5%2C-x%5E2-3x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "we refer to y as the function of x given by y=f(x)= -x^2 - 3x - 2.\"it\"refers to function or y or f(x)<BR>\n" );
document.write( "we find it has two zeros (that is y=0)at x=-1 and x=-2...<BR>\n" );
document.write( "it is  +ve when x is between -1 and -2.<BR>\n" );
document.write( "it is -ve if x<-2...or if x>-1<BR>\n" );
document.write( "its x intercepts are (that is value of x when y is zero )-1 and -2..that is the graph cuts x axis at x=-1 and x=-2<BR>\n" );
document.write( "its y intercept is ( that is value of y when x is zero) is -2<BR>\n" );
document.write( "its vertex is at the point when y is minimum or maximum..for this we write y as follows<BR>\n" );
document.write( "y=-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%283%2F2%29%29%5E2-%282-9%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B%283%2F2%29%29%5E2-%282-9%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%283%2F2%29%29%5E2%2B%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B%283%2F2%29%29%5E2%2B%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now we reason that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%283%2F2%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B%283%2F2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >being perfect square ..it is always positive.hence its minimum value is zero (when x=-3/2)..then y =1/4<BR>\n" );
document.write( "so we call x=0 and y=1/4 as the vertex of the graph. </SPAN>\n" );
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