document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201548>Question 201548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x- and y-intercepts. If no x-intercepts exist, state so.\r<BR>\n" );
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document.write( "f(x) = -x^2 + 7x - 18<BR>\n" );
document.write( " A) No x-intercepts, (0, 18)<BR>\n" );
document.write( " B) No x-intercepts, (0, -18)<BR>\n" );
document.write( " C) ((-x(+ or -)sqrt 121)/(2),0) , (0, -18)<BR>\n" );
document.write( " D) ((-x(+ or -)sqrt 121)/(2),0) , (0, 18)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151805 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=151805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll start with the y-intercept since it is easier. The y-intercept occurs when x=0. (Think about it. All the points along the y-axis have an <b>x-coordinate</b> that is 0.) So to find the y-intercept find the point where x=0, In other words find f(0).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+-%280%29%5E2+%2B+7%280%29+-+18 ALIGN=MIDDLE  ALT=\"f%280%29+=+-%280%29%5E2+%2B+7%280%29+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+-18 ALIGN=MIDDLE  ALT=\"f%280%29+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the y-intercept is (0, 18).<br><BR>\n" );
document.write( "Similarly to find x-intercepts we find we y=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-x%5E2+%2B+7x+-18 ALIGN=MIDDLE  ALT=\"0+=+-x%5E2+%2B+7x+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since this will not factor, we will try the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2+-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. To use this formula we need the values of a, b and c. Since the general form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"0+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will need to rewrite our equation with additions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-1%2Ax%5E2+%2B+7%2Ax+%2B+%28-18%29 ALIGN=MIDDLE  ALT=\"0+=+-1%2Ax%5E2+%2B+7%2Ax+%2B+%28-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From this we can see that<BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "c = -18<BR>\n" );
document.write( "Substituting these values into the quadratic formula we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%287%29+%2B-+sqrt%28%287%29%5E2+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%287%29+%2B-+sqrt%28%287%29%5E2+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%287%29+%2B-+sqrt%2849+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%287%29+%2B-+sqrt%2849+-+4%28-1%29%28-18%29%29%29%2F%282%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%2849+-+72%29%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%2849+-+72%29%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%28-23%29%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28-23%29%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point we can go no farther. When we square any Real number we either get zero or a positive number, <b>never a negative</b>. So it is impossible to square a Real number and get -23. In other words <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-23%29 ALIGN=MIDDLE  ALT=\"sqrt%28-23%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not exist among the Real numbers. This means that there are no x-intercepts on our graph. </SPAN>\n" );
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