To find the y-intercept of the given equation $y^2 = x^3 - 4x$, we need to determine the value of $y$ when $x = 0$.

Let's solve the equation step by step:

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

2. Simplify the equation: $y^2 = 0$

3. Solve for $y$: $y = \sqrt{0}$ $y = 0$

Therefore, the y-intercept of the equation $y^2 = x^3 - 4x$ is $(0, 0)$.

Would you like more details or have any questions?

Here are 8 related questions to further explore this topic:

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

Tip: When dealing with implicit equations, substituting specific values for one variable can simplify the process of finding intercepts and other key points.