Question

The graph of the equation y= x^2-3 is symmetric with respect to which of the following?
a-the x axis
b-the y axis
c-the origin
d-none

Answer 1

Notice how you are in a vertex AND a standard form with this equation at the same time.

Answer 2

y-axis? only a guess XD

Answer 3

If you further wrote the equation as y= (x - 0)^2-3 with an explicit vertex form, you can use that information for your symmetry.

Answer 4

In either form, either an explicit vertex form or the original with an implied vertex form, the "0" will give information about both the actual vertex point and the axis of symmetry.

Answer 5

this doesnt help me any

Answer 6

The answer is contained in what I said. Just read it. It's a parabola opening upward. Think.

Answer 7

You have a minimum at x = 0. It goes up on either side in a mirror-image way.

Answer 8

Test for Symmetry

1. Substitute –y for y, if the equation is unchanged then the curve is symmetrical with respect to the x-axis.
2. Substitute –x for x, if the equation is unchanged the curve is symmetrical with respect to the y- axis.
3. Substitute – x for x and –y for y, if the equation is unchanged then the curve is symmetrical with respect to the origin.


In your case, if we substitute -1 to x^2 then we can see that the equation remains the same, therefore it is symmetric with the y-axis. But if we substitute -1 to y, the equation will change then the equation is not symmetric to the x-axis so it is only symmetric on the y-axis.