The function f(x) = x^2 - 4 is a quadratic equation, which means its graph is a parabola. The term x^2 indicates that the graph opens upwards, while the -4 shifts the entire graph down by 4 units. The vertex of this parabola is at the point (0, -4), which is the lowest point on the graph. To find the roots of the equation, we set f(x) = 0 . This gives us x^2 - 4 = 0 , which can be factored into (x - 2)(x + 2) = 0 . Thus, the solutions are x = 2 and x = -2 , meaning the graph intersects the x-axis at these points.