Question

The graph of 6x2=y-1 is symmetric with respect which of the following?

Answer 1

The graph of 6x2=y-1 is symmetric with respect to the y-axis

Explanation:

The symmetry of a function can be evaluated graphically or analytically.

If a function is symmetric with respect to the y-axis then substituting -x in place of x should yield the same equation. In this case we have;

`6x^(2) =y-1\\6(-x)^(2) =y-1\\6x^(2) =y-1`

The equation is identical to the original one.

Answer 2

Option d. symmetric about y-axis is the correct answer.

Explanation:

The given equation of the graph is 6x² = y - 1

y = 6x² + 1

To check the symmetry of any function about y axis we replace x with (-x). If the new equation is exactly same as the original function or equation then the graph is symmetric to the y axis.

By replacing x with (-x) in the equation

y = 6×(-x)²+1

y = 6x² + 1

which is same as the original one and symmetric to y-axis

Now by replacing y by (-y)

-y = 6x² + 1

This equation is not matching the original equation.

Therefore the graph is non symmetric to the x-axis.

Option d. is the correct answer.