Question

Skylar is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by y = x^2, where x and y are measured in inches. What is the focus of the flashlight? Option 1: (–5, 1) Option 2: (–2, –5) Option 3: (1, –5) Option 4: (5, 1)

Answer 1

The focus of the flashlight designed by Skylar using the parabolic reflecting mirror with the equation y = x^2 is (0, 1/4).

Step-by-step explanation:

The shape of the mirror in the flashlight can be modeled by the equation y = x^2. This equation represents a parabola with a vertical axis of symmetry. The focus of a parabola is a point along the axis of symmetry where all incoming light rays parallel to the axis are reflected and converge.

In this case, the equation y = x^2 has a positive coefficient for x^2, which means its axis of symmetry lies along the y-axis. The focus of the flashlight can be determined by using the formula F = (0, 1/4a), where a is the coefficient of x^2. In this case, a = 1, so the focus is located at (0, 1/4).

Therefore, none of the given options are correct. The focus of the flashlight should be (0, 1/4).

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