To find the y-intercept of a quadratic equation, you set \(x = 0\) and solve for \(y\). For the equation \(y = x^2 - 2x - 8\):

\[ y = (0)^2 - 2(0) - 8 \]
\[ y = -8 \]

Therefore, the y-intercept is at the point \((0, -8)\).

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### Follow-up Questions:
1. How do you interpret the y-intercept in the context of a real-world problem?
2. What role does the y-intercept play in graphing quadratic functions?
3. How can you determine the x-intercepts from the quadratic formula?
4. What are the different methods to find the roots of a quadratic equation?
5. Can a quadratic function have more than one y-intercept?
6. How do the coefficients in the standard form of a quadratic equation affect its graph?
7. What is the importance of the discriminant in determining the nature of the roots?
8. How can completing the square help in finding the vertex of a quadratic function?

**Tip:** The y-intercept gives you the starting value of a function when \(x = 0\). It's often helpful as a reference point when graphing.

Explore how to find the y-intercept of a quadratic equation with detailed steps and examples. This problem covers key concepts like quadratic equations, y-intercept determination, and its role in graphing functions. Suitable for high school students.

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