Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the origin. Where should Gabe place the bulb to ensure a perfect beam of light?

The mirror’s rim is 4 inches across, so its edge is 2 inches from the center: the parabola passes through (2, 1). For an upward-opening parabola with vertex at the origin, x² = 4py, where the focus is (0, p). Substituting (2, 1) gives 4 = 4p, so p = 1. Gabe should place the bulb at the focus, (0, 1), which is choice C.

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