document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297565>Question 297565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the quadratic function <BR>\n" );
document.write( "f(x) = -x2 + 1<BR>\n" );
document.write( "Describe the correct graph and why...Which way does the parabola go up or down, where does the graph cross the x-axis and y-axis....<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 #214273 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph the quadratic function <BR>\n" );
document.write( "f(x) = -x^2 + 1<BR>\n" );
document.write( "Describe the correct graph and why...Which way does the parabola go up or down, where does the graph cross the x-axis and y-axis....\r<BR>\n" );
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document.write( "The graph points up and opens down.\r<BR>\n" );
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document.write( "Standard form of quadratic equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "Set f(x) = to 0 and you have this equation in standard form.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "-x^2 + 1 = 0\r<BR>\n" );
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document.write( "In this equation:\r<BR>\n" );
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document.write( "a = -1<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "c = 1\r<BR>\n" );
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document.write( "Maximum point is at x = -b/2a which becomes 0\r<BR>\n" );
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document.write( "When x = 0, y = 1, so the maximum point is (x,y) = (0,1).\r<BR>\n" );
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document.write( "To find the points where this graph crosses the x-axis, you have to solve the equation -x^2 + 1 = 0\r<BR>\n" );
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document.write( "With this equation, you subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "-x^2 = -1\r<BR>\n" );
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document.write( "Multiply both sides of this equation by -1 to get:\r<BR>\n" );
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document.write( "x^2 = 1\r<BR>\n" );
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document.write( "Take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "x = +/- 1\r<BR>\n" );
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document.write( "Those should be the x-axis crossing points.\r<BR>\n" );
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document.write( "You could also have factored the equation of -x^2 + 1 = 0 to get:\r<BR>\n" );
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document.write( "(-x+1) * (x+1) = 0\r<BR>\n" );
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document.write( "When either of these factors = 0, the equation is grue, so you set each of the factors equal to 0 and solve.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "x = -1 and x = 1.\r<BR>\n" );
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document.write( "You graph this equation by plotting some values of x and getting corresponding values of y.\r<BR>\n" );
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document.write( "You start with x = -1, x = 0, x = 1\r<BR>\n" );
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document.write( "That should be enough to draw a rough graph, but you might want to fill in some additional points to fit the curve better.\r<BR>\n" );
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document.write( "Your graph should look like this:\r<BR>\n" );
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