document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214914>Question 214914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function<BR>\n" );
document.write( "the equation is: -x(x-3)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162370 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=162370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function<BR>\n" );
document.write( "the equation is: -x(x-3)<BR>\n" );
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document.write( "Equation: y = -x(x-3) = -x^2 + 3x<BR>\n" );
document.write( "a = -1; b = 3 ; c = 0<BR>\n" );
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document.write( ":(a) determine whether the graph opens down or up, <BR>\n" );
document.write( "Answer: Down because a is negative, so as x gets larger <BR>\n" );
document.write( "-x^2 gets more negative.<BR>\n" );
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document.write( "(b) find the axis of symmetry, <BR>\n" );
document.write( "Ans: The equation of the axis of symmetry is x = -b/2a<BR>\n" );
document.write( "x = -3/(2*-1) = 3/2<BR>\n" );
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document.write( "(c)find the vertex, <BR>\n" );
document.write( "Ans: Vertex occurs where x = -b/2a = 3/2<BR>\n" );
document.write( "f(x) = -x^2 + 3x<BR>\n" );
document.write( "Find the y-value: f(3/2) = -(3/2)^2+3(3/2)<BR>\n" );
document.write( "f(3/2) = -(9/4)+9/2 = -9/4 + 18/4 = 9/4<BR>\n" );
document.write( "So the vertex is (3/2 , 9/4)<BR>\n" );
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document.write( "(d)find the y-intercept,\r<BR>\n" );
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document.write( "y = -x^2+3x<BR>\n" );
document.write( "To find the y-intercept let x=0.<BR>\n" );
document.write( "Then y = -0^2+3*0 = 0+0 = 0<BR>\n" );
document.write( "So the y-intercept is (0,0) or simply zero.<BR>\n" );
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document.write( "(e) find the zeros, <BR>\n" );
document.write( "Let y = 0 and solve for \"x\":<BR>\n" );
document.write( "-x^2+3x = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "-x(x-3)=0<BR>\n" );
document.write( "-x = 0 or x-3 = 0<BR>\n" );
document.write( "x = 0 or x = 3<BR>\n" );
document.write( "Those are the zeroes.<BR>\n" );
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document.write( "(f) graph the function<BR>\n" );
document.write( "Need to plot several points by giving a value for \"x\"<BR>\n" );
document.write( "and finding the y-value associated with that x-value.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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