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To find the x-intercepts of the curve $y = x^2 - 4$, set the function equal to zero ($x^2 - 4 = 0$) and factor the expression as a difference of squares into $(x+2)(x-2) = 0$. Applying the zero-product property yields the solutions $x = -2$ and $x = 2$, which are the points where the graph crosses the x-axis.

Conditions: The curve is defined by the quadratic equation $y = x^2 - 4$.; The goal is to find where the graph crosses the x-axis.; The algebraic method used is factoring the difference of perfect squares.

To find the x-intercepts of the curve $y = x^2 - 4$, set the function equal to zero ($x^2 - 4 = 0$) and factor the expression as a difference of squares into $(x+2)(x-2) = 0$. Applying the zero-product property yields the solutions $x = -2$ and $x = 2$, which are the points where the graph crosses the x-axis.

Conditions: The curve is defined by the quadratic equation $y = x^2 - 4$.; The goal is to find where the graph crosses the x-axis.; The algebraic method used is factoring the difference of perfect squares.