document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144449>Question 144449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I barely even know how to find the quadratic formula of f(x), i don't even know if i can find the roots of this given function, and then graph the function of  g(x) = x2 - x - 12. What do i do just to get started on this someone. Any help would be appreciated. Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105185 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=105185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This will be a pseudo-lesson of factoring and graphing. Do not become afraid of all the letters I use in the general case...\r<BR>\n" );
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document.write( "Factor first: <BR>\n" );
document.write( "x^2-x-12\r<BR>\n" );
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document.write( "If we can factor a quadratic it will generally be in form:<BR>\n" );
document.write( "(ax+b)(cx+d)<BR>\n" );
document.write( "Now if we apply FOIL to that:<BR>\n" );
document.write( "acx^2+dax+bcx+bd<BR>\n" );
document.write( "=acx^2+(da+bc)x+bd\r<BR>\n" );
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document.write( "As you can see, the number in front of the x term is the sum of da and bc. On the other hand, the \"loose\" term, that is, the one without an x, is the product bd.\r<BR>\n" );
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document.write( "So we want -1=da+bc and -12=bd.<BR>\n" );
document.write( "We can achieve this by listing the factors of -12 and seeing which add to -1 (when one is made negative). <BR>\n" );
document.write( "12=1*2*2*3     which means 1,2,3,4,6,and 12 are factors. Now, we can see that -4+3=-1, and -4*3=-12. These have to be the two factors!\r<BR>\n" );
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document.write( "So, x^2-x-12=(x-4)(x+3).\r<BR>\n" );
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document.write( "Now, to find the zeros/solutions, we set that =0. <BR>\n" );
document.write( "(x-4)(x+3)=0.<BR>\n" );
document.write( "This is saying that one quantity times another is 0. So, one or both quantities have to be 0.<BR>\n" );
document.write( "So x-4=0 or x+3=0<BR>\n" );
document.write( "x=4 or x=-3. These are the points where the y-value is zero.<BR>\n" );
document.write( "So (4,0), (-3,0) are the x-intercepts.\r<BR>\n" );
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document.write( "The y-intercept is found by setting x=0.<BR>\n" );
document.write( "This gives -4*3=-12. So (0,-12) is the y-intercept.\r<BR>\n" );
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document.write( "Moreover, the vertex is given by x=-b/(2a) for ax^2+bx+c=0 form. So we have x=1/2 is the vertex. f(1/2)=1/4-1/2-12=-49/4 gives the y value of the vertex.\r<BR>\n" );
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document.write( "Lastly, the function will open upward because the leading coefficient of x^2 is positive.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-10%2C+10%2C+-15%2C+10%2C+x%5E2-x-12+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-10%2C+10%2C+-15%2C+10%2C+x%5E2-x-12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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