Question

The reflector of a flashlight is in the shape of a parabolic surface. The reflector has a diameter of 16 centimeters and a depth of 8 centimeters. How far from the vertex should the light bulb be placed?

a) 8 centimeters
b) 4 centimeters
c) 12 centimeters
d) 16 centimeters

The equation of the function g(x) that is a reflection of the graph of the f(x) about the x-axis is given by which of the following?

a) g(x) = 1/f(x)
b) g(x) = -f(x)
c) g(x) = f(-x)
d) g(x) = f(x)

Answer 1

The light bulb should be placed 8 centimeters from the vertex of the parabolic reflector. The equation of the function g(x) that is a reflection of the graph of the f(x) about the x-axis is given by g(x) = f(-x).

Step-by-step explanation:

The reflector of a flashlight is in the shape of a parabolic surface. The reflector has a diameter of 16 centimeters and a depth of 8 centimeters. To find the distance from the vertex to the light bulb, we need to determine the focal length of the parabolic reflector. The focal length of a parabola is half of its diameter, so the focal length in this case is 8 centimeters. Therefore, the light bulb should be placed 8 centimeters from the vertex of the parabolic reflector.

The equation of the function g(x) that is a reflection of the graph of the f(x) about the x-axis is given by g(x) = f(-x). This means that to reflect the graph of f(x) about the x-axis, we substitute -x for x in the equation.