The vertex of the parabola occurs at (1/4, 0) or (0.25, 0). Since the coefficient of x^2 is a positive number, then it the parabola opens upward. The vertex is the minimum point on the graph, which happens to occur along the x-axis at (1/4, 0) as the only x-intercept.
Therefore, the graph intersects the x-axis only once, at the vertex.
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