Which equation has an axis of symmetry at x = 0?

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To determine which equation has an axis of symmetry at x = 0, we need to consider the properties of various equations, primarily focusing on quadratic equations.

The standard form of a quadratic equation is:

y = ax² + bx + c

In this case, the axis of symmetry can be found using the formula:

x = -b / (2a)

For the axis of symmetry to be x = 0, the equation must satisfy:

0 = -b / (2a)

This implies that b must be equal to 0. Therefore, the quadratic equation reduces to:

y = ax² + c

With b = 0, the equation is a function of x² only, meaning it is symmetrical about the y-axis, which corresponds with an axis of symmetry at x = 0.

For example, consider the following equation:

y = 2x² + 3

In this quadratic function, there is no linear term (the bx term), so it is symmetrical around the y-axis. Thus, it has an axis of symmetry at x = 0.

In conclusion, any quadratic equation of the form y = ax² + c will have its axis of symmetry at x = 0 when the coefficient of the linear term is zero.

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