Gabriella 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. where should she place the bulb to ensure a perfect beam of light?

Gabriella should place the bulb at (0,1).

Step-by-step explanation:

It is given that the Gabriella 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.

For the perfect light beams she has to place the bulb at focus of the parabola.

It is an upward parabola, therefore the vertex is origin.

The point (2,1) and (-2,1) lies on the parabola, therefore

The focus is (0,a), therefore the focus is (0,1)

The focus is 1 in. upward from the vertex, therefore Gabriella should place the bulb at (0,1).

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