document.write( "Question 485854: how do you make a table and graph the function f(x)=1/2 of x squared \n" ); document.write( "

Algebra.Com's Answer #332251 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
your equation is y = x^2/2
\n" ); document.write( "your graph would look like this:
\n" ); document.write( " $\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2F2%29\"$
\n" ); document.write( "you set up a table with values of x and corresponding values of y.
\n" ); document.write( "your table would look like this:
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document.write( "x	y = x^2/2\r\n" );
document.write( "-10	50\r\n" );
document.write( "-9	40.5\r\n" );
document.write( "-8	32\r\n" );
document.write( "-7	24.5\r\n" );
document.write( "-6	18\r\n" );
document.write( "-5	12.5\r\n" );
document.write( "-4	8\r\n" );
document.write( "-3	4.5\r\n" );
document.write( "-2	2\r\n" );
document.write( "-1	0.5\r\n" );
document.write( "0	0\r\n" );
document.write( "1	0.5\r\n" );
document.write( "2	2\r\n" );
document.write( "3	4.5\r\n" );
document.write( "4	8\r\n" );
document.write( "5	12.5\r\n" );
document.write( "6	18\r\n" );
document.write( "7	24.5\r\n" );
document.write( "8	32\r\n" );
document.write( "9	40.5\r\n" );
document.write( "10	50\r\n" );
document.write( "

\n" ); document.write( "if you knew the shape of the curve, you might have been able to get by with plotting less values of x and then finding the corresponding value of y by using the equation.\r
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\n" ); document.write( "\n" ); document.write( "example:
\n" ); document.write( "equation is y = x^2/2
\n" ); document.write( "when x is equal to 5, y is equal to 5^2/2 = 25/2 = 12.5\r
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\n" ); document.write( "\n" ); document.write( "since y = x^2 is a form of the quadratic equation, then you could have determined the general shape just from that fact alone.\r
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\n" ); document.write( "\n" ); document.write( "you do need to be familiar with what the graph of a quadratic equation looks like in order to be able to minimize the number of points you need to sketch the graph.\r
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\n" ); document.write( "\n" ); document.write( "if in doubt, start with x = 0 and work up and down in increments of 1 to see if a shape develops.\r
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\n" ); document.write( "\n" ); document.write( "sometimes you need more values of x to see if a shape develops.\r
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\n" ); document.write( "\n" ); document.write( "in this case, x from -5 to + 5 would probably have been enough.\r
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\n" ); document.write( "\n" ); document.write( "jumping to x = -10 and x = +10 would have been enough to show that it's was following the same trajectory as the values of x got bigger or smaller.\r
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\n" ); document.write( "\n" ); document.write( "the minimum point is at x = 0.\r
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\n" ); document.write( "\n" ); document.write( "you could see a change in direction when you plotted values of x = 0, then x = -1, then x = 1.\r
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