document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=454646>Question 454646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem:\r<BR>\n" );
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document.write( "Determine the parameter k so that the quadratic equation k x^2-16x+16=0 had exactly one real solution.\r<BR>\n" );
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document.write( "A world problem is related to this problem too: An object is tossed into the air with an upward velocity of 22 feet per second from the top of a 10-foot wall. Its flight is governed by h(t)=16t^2-22t-10=0. What is the time for the object to reach the highest point, and what is the altitude of this highest point?\r<BR>\n" );
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document.write( "Thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312180 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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/cgi-bin/show-face.mpl?user=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=312180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the parameter k so that the quadratic equation k x^2-16x+16=0 had exactly one real solution.<BR>\n" );
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document.write( "From the quadratic formula the zeros are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In order for there to be only one real zero, the discriminant <BR>\n" );
document.write( "<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;\" > must equal zero.<BR>\n" );
document.write( "In this case, a = k, so we have<BR>\n" );
document.write( "16^2 - 4*k*16 = 0<BR>\n" );
document.write( "16 = 4k<BR>\n" );
document.write( "This gives k = 4<BR>\n" );
document.write( "As a check, we plot the graph, and confirm that the vertex lies on the x-axis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C6%2C-20%2C20%2C4x%5E2-16x%2B16%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-6%2C6%2C-20%2C20%2C4x%5E2-16x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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