SOLUTION: Can someone please show me how to graph the equation y=1/2x^2+1 using symmetric properties?

Algebra ->  Algebra  -> Graphs -> SOLUTION: Can someone please show me how to graph the equation y=1/2x^2+1 using symmetric properties?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 596732: Can someone please show me how to graph the equation y=1/2x^2+1 using symmetric properties?
Answer by KMST(1860) About Me  (Show Source):
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.
f%28-x%29=f%28x%29
Functions that do that are called even functions and are symmetrical with respect to the y-axis.
The y-axis is the line x=0.
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.
For x=0, y=%281%2F2%290%5E2%2B1=0%2B1=1, which gives you the point (0,1).
For x=2, y=%281%2F2%292%5E2%2B1=4%2F2%2B1=2%2B1=3, which gives you the point (2,3).
For x=4, y=%281%2F2%294%5E2%2B1=16%2F2%2B1=8%2B1=9, which gives you the point (4,9).
No calculations are required for the symmetrical points (-2,3) and (-4,9); you just change the sign of the x coordinate.
Next, plot the five points and then draw a reasonable line
graph%28300%2C300%2C-5%2C5%2C-1%2C11%2Cx%5E2%2F2%2B1%29
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.