document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199101>Question 1199101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the parabola  y=x^2 +4x -3.<BR>\n" );
document.write( "Find the coordinates of the focus.\r<BR>\n" );
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document.write( "The correct answer is one of the following. Which one is correct?\r<BR>\n" );
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document.write( "A) (-2,-6.75)\r<BR>\n" );
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document.write( "B) (2,6.75)\r<BR>\n" );
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document.write( "C) (-2,-6)\r<BR>\n" );
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document.write( "D) (-2,-5.75) </SPAN>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B4x-3 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B4x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Complete the square to put the equation in vertex form.  Vertex form is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The vertex is (h,k); p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B4x%2B4%29-3-4 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B4x%2B4%29-3-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E2-7 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E2-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The vertex is (-2,-7); 1/(4p) = 1, so p = 1/4.<br><BR>\n" );
document.write( "The parabola opens upward, so the focus is p units above the vertex: -7 + 1/4 = -6.75.<br><BR>\n" );
document.write( "ANSWER A) (-2,-6.75)<br><BR>\n" );
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