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.

Learn how to find the y-intercept of the cubic equation y^2 = x^3 - 4x with a detailed step-by-step solution. This problem involves algebraic concepts such as cubic equations and intercepts. Suitable for advanced high school students.

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