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Determine whether the graph of y=3+x^2 is symmetric with respect to the x-axis, the y-axis or the origin.

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2 Answers

Hi Kimberly, 
 
For this question first you need to take a set of values for 'x' so that you can plug in those values in the equation  y = 3 + x^2 to find y.
 
Here are values I took for 'x' and computed values for 'y' based on them:
 
x      -2, -1, 0, 1, 2
y       7,  4,  3, 4, 7
 
 
Now if you see, the values of y remain the same for the -2 and 2 and -1 and 1.
 
And if you plot all the values of x and y on the graph, it would result in a curve which is symmetric to 'y' axis.
 
 
Hope this helps! :)

 Y = X2  + 3

 

  To Test That:

 

    X = -1  Y = 4    X = 1  Y = 4

    All points of ( -2, 7) & ( 2, 7) , (- 3, 12)& ( 3, 12) ......( -n, n2 +3)& ( n , n2 +3)

   all lie on the curve of the X+ 3 , therefore, the function is Symmetric to Y -axis.

    In general quadratic aX+ bX + c  has axis of Symmetry of X= -b/2a

   In this case y =x+ 3, where b=0 , and a =1 axis of symmetry is  X =0/2 =0

    X= 0 , Y axis is axis of Symmetry.

   axis.