document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119491>Question 119491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadratic function h(x) has zeros at 4 and -3 and a y intercept of -12. The function h(x) is translated -3 units on the x axis. Which of the following equations represents g(x), the transformed h(x)?\r<BR>\n" );
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document.write( "a. g(x) = x^2 - 5x\r<BR>\n" );
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document.write( "b. g(x) = x^2 + 7x\r<BR>\n" );
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document.write( "c. g(x) = x^2 -x -15\r<BR>\n" );
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document.write( "d. g(x) = x^2 + 5x - 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87546 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=87546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadratic function h(x) has zeros at 4 and -3 and a y intercept of -12. The function h(x) is translated -3 units on the x axis. Which of the following equations represents g(x), the transformed h(x)? <BR>\n" );
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document.write( "Find the equation of the quadratic before it is transformed:<BR>\n" );
document.write( "y = a(x-4)(x+3)<BR>\n" );
document.write( "Substitute (0,-12) to find \"a\"<BR>\n" );
document.write( "-12 = a(0-4)(0+3)<BR>\n" );
document.write( "-12 = -12a<BR>\n" );
document.write( "a = 1<BR>\n" );
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document.write( "Original equation is y = x^2-x-12<BR>\n" );
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document.write( "To translate -3 on the x-axis substitute (x+3) for x to get<BR>\n" );
document.write( "the new equation:<BR>\n" );
document.write( "y = (x+3)^2-(x+3)-12<BR>\n" );
document.write( "y = x^2+6x+9-x-3-12<BR>\n" );
document.write( "y = x^2+5x-6<BR>\n" );
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document.write( "Graph the two equations to see the effect of the translation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-20%2C10%2Cx%5E2-x-12%2Cx%5E2%2B5x-6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-20%2C10%2Cx%5E2-x-12%2Cx%5E2%2B5x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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