document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147711>Question 147711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help!<BR>\n" );
document.write( "1.  write the equation of a line whose slope is -2 and passes through (-1,6).  Write answer in slope-intercept form.\r<BR>\n" );
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document.write( "2.  Solve for x:  (2x-7)(x+4)=0\r<BR>\n" );
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document.write( "3.  find the vertex of f(x)=3x^2-6x+8\r<BR>\n" );
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document.write( "4. find the y-intercept of the cubic f(x)=(x-2)(x+1)(x-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108096 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. y=mx+b where m is the slope and b is the y-intercept (what y is when x is zero).  So y=-2x+b. To find b, you know that the slope is rise/run or -2/1.  So take the point (-1,6) and add 1 to x and subtract 2 from y. You get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2C4 ALIGN=MIDDLE  ALT=\"0%2C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the y-intercept is 4. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B4 ALIGN=MIDDLE  ALT=\"y=-2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2. (2x-7)(x+4)=0. Just take each expression separately and set each one equal to zero.  what minus seven equals zero? Seven. So you know 2x=7.  So x there is 7/2.  What plus four equals zero? x=-4 there. So the solutions for this equation are x=7/2;-4.\r<BR>\n" );
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document.write( "3.find the vertex of f(x)=3x^2-6x+8. vertex: the value of y that does not repeat.  To get this, plug in a few consecutive values of x and see which one does not repeat an answer.  That would be the vertex.  In this case, I will let you know that it is at (1,5). Because:<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=3x%5E2%2B-6x%2B8+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-6x%2B8+=+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" );
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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" );
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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=%28-6%29%5E2-4%2A3%2A8=-60 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-6%29%5E2-4%2A3%2A8=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  The discriminant -60 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -60 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+60%29+=+7.74596669241483 ALIGN=MIDDLE  ALT=\"sqrt%28+60%29+=+7.74596669241483\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--6%2B-+i%2Asqrt%28+-60+%29%29%2F2%5C3+=++%28--6%2B-+i%2A7.74596669241483%29%2F2%5C3+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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+3%2Ax%5E2%2B-6%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-6%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "5 is the only y value that does not repeat.\r<BR>\n" );
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document.write( "4. find the y-intercept of the cubic f(x)=(x-2)(x+1)(x-3). y=f(x), so that means find f(0), because the y-intercept is what y is when x is 0.  So plug in 0 and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280-2%29%280%2B1%29%280-3%29 ALIGN=MIDDLE  ALT=\"f%280%29=%280-2%29%280%2B1%29%280-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%28-2%29%281%29%28-3%29 ALIGN=MIDDLE  ALT=\"f%280%29=%28-2%29%281%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiply it all out and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the y-intercept is 6. </SPAN>\n" );
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