document.write( "Question 596732: Can someone please show me how to graph the equation y=1/2x^2+1 using symmetric properties? \n" ); document.write( "

Algebra.Com's Answer #378019 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The function $\"f%28x%29=%281%2F2%29x%5E2%2B1\"$ takes the same value for x as for -x.
\n" ); document.write( " $\"f%28-x%29=f%28x%29\"$
\n" ); document.write( "Functions that do that are called even functions and are symmetrical with respect to the y-axis.
\n" ); document.write( "The y-axis is the line $\"x=0\"$ .
\n" ); document.write( "You can get five points if you just calculate the value of the function at x=0, and at a couple of positive x values. You get the symmetrical points on the side with negative x for free.
\n" ); document.write( "For x=0, $\"y=%281%2F2%290%5E2%2B1=0%2B1=1\"$ , which gives you the point (0,1).
\n" ); document.write( "For x=2, $\"y=%281%2F2%292%5E2%2B1=4%2F2%2B1=2%2B1=3\"$ , which gives you the point (2,3).
\n" ); document.write( "For x=4, $\"y=%281%2F2%294%5E2%2B1=16%2F2%2B1=8%2B1=9\"$ , which gives you the point (4,9).
\n" ); document.write( "No calculations are required for the symmetrical points (-2,3) and (-4,9); you just change the sign of the x coordinate.
\n" ); document.write( "Next, plot the five points

and then draw a reasonable line
\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-1%2C11%2Cx%5E2%2F2%2B1%29\"$
\n" ); document.write( "Doing it with pencil and paper, show my calculations first, with few, if any, words. Then I would have the line with the points clearly marked on just one graph, and I would include a table with the x and y values next to the graph. However, you should do it in whatever style your teacher prefers.
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