document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087736>Question 1087736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the quadratic inequality. Write the solution set in interval notation.Please show  your complete step by step solution. <BR>\n" );
document.write( "y^2-17y+70<0<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 #702031 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=702031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> set it equal to 0 and factor.\r<BR>\n" );
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document.write( "you get y^2 - 17y + 70 = 0 becomes (y - 7) * (y - 10) = 0\r<BR>\n" );
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document.write( "set each factor to 0 and you get:\r<BR>\n" );
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document.write( "y - 7 = 0<BR>\n" );
document.write( "y - 10 = 0\r<BR>\n" );
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document.write( "solve for y and you get:\r<BR>\n" );
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document.write( "y = 7<BR>\n" );
document.write( "y = 10\r<BR>\n" );
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document.write( "the value of the equation is equal to 0 when y = 7 and y = 10\r<BR>\n" );
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document.write( "look for the area where:\r<BR>\n" );
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document.write( "y < 7<BR>\n" );
document.write( "y > 10<BR>\n" );
document.write( "y > 7 and < 10 which can be shown as 7 < y < 10\r<BR>\n" );
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document.write( "pick any values of y in those areas.\r<BR>\n" );
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document.write( "i chose y = 5, y = 15, y = 8\r<BR>\n" );
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document.write( "when y = 5, the equation = 10 which is  positive.\r<BR>\n" );
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document.write( "when y = 15, the equation = 40 which is positive.\r<BR>\n" );
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document.write( "when y = 8, the equation = -2 which is negative.\r<BR>\n" );
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document.write( "since the equation is continuous, it will remain negative until it crosses a zero point at which time it will remain positive until it reaches another zero point, and vice versa.\r<BR>\n" );
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document.write( "therefore y > 0 when y < 7 and y > 10, and y < 0 when 7 < y < 10.\r<BR>\n" );
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document.write( "in interval notation, this would look like this:\r<BR>\n" );
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document.write( "equation is greater than 0 when y = (minus infinity,7) union (10, plus infinity)\r<BR>\n" );
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document.write( "this translates to the value of y is between minus infinity and 7, or between 10 and plus infinity, but does not include 7, 10, or infinity (plus or minus).\r<BR>\n" );
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document.write( "equation is less than 0 when y = (7,10)\r<BR>\n" );
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document.write( "this translates to the value of y is between 7 and 10, but does not include 7 or 10.\r<BR>\n" );
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document.write( "equation is equal to 0 when y = [7,7] union [10,10]\r<BR>\n" );
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document.write( "this translates to the value of y is equal to 7 or equal to 10.\r<BR>\n" );
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document.write( "graphically, the equation would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/071501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the y-axis is at x = 0<BR>\n" );
document.write( "the x-axis is at y = 0\r<BR>\n" );
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document.write( "the coordinates are shown as (x,y)\r<BR>\n" );
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document.write( "for example, (40,15) means that the value of x is 40 when the value of y is 15.\r<BR>\n" );
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document.write( "x represents the value of the equation.\r<BR>\n" );
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document.write( "for example, (40,15) means that the value of the equation is 40 when the value of y is 15.\r<BR>\n" );
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document.write( "the equation used for graphing is x = y^2 - 17x + 70\r<BR>\n" );
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