Let's analyze and solve the problem step by step.

The given equation is: $y = x^2 - 3x - 4$ To find the x-intercepts, we set $y = 0$ and solve for $x$.

$0 = x^2 - 3x - 4$ This is a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula. Let's factor it first:

$x^2 - 3x - 4 = (x - 4)(x + 1) = 0$ Setting each factor to zero gives: $x - 4 = 0 \quad \text{or} \quad x + 1 = 0$ Thus: $x = 4 \quad \text{or} \quad x = -1$

So, the x-intercepts are $x = 4$ and $x = -1$.

Answer: The x-intercepts are $x = -1$ and $x = 4$.

Do you have any further questions, or would you like more details on any part of this?

Here are 5 related questions you might consider:

1. How do you find the y-intercept of a quadratic equation?
2. What is the quadratic formula, and when would you use it?
3. Can all quadratic equations be factored?
4. How do you determine the vertex of the parabola for a quadratic function?
5. What is the significance of the discriminant in a quadratic equation?

Tip: To solve quadratic equations easily, try factoring first, and if it's not factorable, use the quadratic formula!