The y-intercept of the graph represented by the equation $y = x^2 - 4$ is given by the value $-4$.

To determine the y-intercept of a graph, you must find the value of $y$ when $x$ is equal to $0$. The y-intercept is the point at which the graph intersects the y-axis, and at this intersection, the value of $x$ is always $0$.

For the equation $y = x^2 - 4$, we substitute $x = 0$ into the equation:

This simplifies to:

Thus, when $x = 0$, we find that $y = -4$. This indicates that the graph crosses the y-axis at the point $(0, -4)$. Therefore, we can conclude that the y-intercept is $-4$.

Understanding the y-intercept is essential, as it provides a crucial starting point for graphing the equation. In this instance, the graph is a parabola that opens upwards, since the coefficient of $x^2$ is positive. Knowing the y-intercept allows for a more accurate plotting of the graph and enhances your comprehension of its behavior. For GCSE Maths, the ability to identify and interpret the y-intercept is a fundamental skill that will significantly assist you in solving and graphing quadratic equations.