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?

At the mirror’s rim, the parabola is 1 inch above its vertex and 2 inches from the axis, since the 4-inch diameter gives a radius of 2 inches. Using the standard form x² = 4py, the point (2, 1) gives 4 = 4p, so p = 1. The focus is (0, p), so Gabe should place the bulb at (0, 1), choice A.

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