document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193021>Question 1193021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State two different ways to determine the number of zeros of the function \r<BR>\n" );
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document.write( "f(x)=2(x+1)^2 -6 </SPAN>\n" );
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document.write( "Technically, it is a polynomial of degree 2, so it has 2 zeros.<br><BR>\n" );
document.write( "If you mean real zeros, then....<br><BR>\n" );
document.write( "(1) Convert the equation to standard form <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;\" > and look at 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;\" >.  There are 2 zeros if the discriminant is positive, 1 zero if it is 0, and no (real) zeros if it is negative.<br><BR>\n" );
document.write( "(2) The equation as given is in vertex form.  The vertex is (-1,-6) and the parabola opens upward, so there are 2 real zeros.<br><BR>\n" );
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