To find the x-intercept(s) of the equation $y^2 = x^3 - 4x$, we need to determine the values of $x$ when $y = 0$.

Let's solve the equation step by step:

1. Substitute $y = 0$ into the equation: $0^2 = x^3 - 4x$

2. Simplify the equation: $0 = x^3 - 4x$

3. Factor the equation: $0 = x(x^2 - 4)$ $0 = x(x - 2)(x + 2)$

4. Solve for $x$: $x = 0 \quad \text{or} \quad x = 2 \quad \text{or} \quad x = -2$

Therefore, the x-intercepts of the equation $y^2 = x^3 - 4x$ are $(0, 0)$, $(2, 0)$, and $(-2, 0)$.

Would you like more details or have any questions?

Here are 8 related questions to further explore this topic:

1. How do you find the vertex of the curve defined by $y^2 = x^3 - 4x$?
2. What are the symmetry properties of the curve $y^2 = x^3 - 4x$?
3. Can you find the points of intersection between $y^2 = x^3 - 4x$ and another curve, such as $y = x$?
4. What is the general approach to finding the tangents to the curve $y^2 = x^3 - 4x$?
5. How do you determine if the curve $y^2 = x^3 - 4x$ has any asymptotes?
6. How do you solve $y^2 = x^3 - 4x$ for $y$ in terms of $x$?
7. How does the curve $y^2 = x^3 - 4x$ compare to a standard parabola or cubic function?
8. What is the significance of the discriminant in determining the nature of the roots of the equation $x^3 - 4x = 0$?

Tip: When solving polynomial equations, factoring is a powerful tool for finding roots. If factoring is difficult, consider using the quadratic formula or other algebraic techniques.