document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090556>Question 1090556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI can someone please help me out with this question? you don't have to answer everything if you don't want to. anything helps. thank you so much<BR>\n" );
document.write( "A quadratic function is defined by f(x)=-3.7x^2+6.8x+4.2. A linear function is defined by g(x) = –0.5x + k.                <BR>\n" );
document.write( "a) Determine the A quadratic function is defined by  . A linear function is defined by g(x) = –0.5x + k.                value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth<BR>\n" );
document.write( "b)Determine the values of k so that the line intersects the parabola at two points.<BR>\n" );
document.write( "c) Determine the values of k so that the line never intersects the parabola.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704998 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Set the two functions equal to each other to find where they intersect.  You end up with a quadratic function that involves the parameter k.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.7x%5E2%2B6.8x%2B4.2+=+-0.5x+%2B+k ALIGN=MIDDLE  ALT=\"-3.7x%5E2%2B6.8x%2B4.2+=+-0.5x+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.7x%5E2%2B7.3x%2B%284.2-k%29+=+0 ALIGN=MIDDLE  ALT=\"-3.7x%5E2%2B7.3x%2B%284.2-k%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You want the parabola and the line to intersect at exactly one point.  That means you want this quadratic equation to have a single solution.  It has a single solution when the discriminant in the quadratic formula,<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;\" ><BR>\n" );
document.write( "is equal to 0.  So solve for k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287.3%29%5E2+-+4%28-3.7%29%284.2-k%29=0 ALIGN=MIDDLE  ALT=\"%287.3%29%5E2+-+4%28-3.7%29%284.2-k%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I will let you finish that part... since you said it was okay if I didn't answer everything.  Besides, you will learn more from this if you do some of the work yourself.<br><BR>\n" );
document.write( "Then answering the other two questions is easy.<br><BR>\n" );
document.write( "Since k is the y-intercept of the linear function, and since the parabola opens downward, any value of k smaller than the one that gives a single intersection point will give 2 intersection points, and any value larger will give 0 intersection points. </SPAN>\n" );
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