An engineer sketches a design for a flashlight that uses a mirror in the shape of a parabola to maximize the output of the light. The function representing the mirror is graphed on the left. Which function models the situation? f(x) = (x – 6)2 2 f(x) = –(x – 0)2 20 f(x) = 3(x – 6)2 2 f(x) = –3(x – 0)2 20.

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

[tex]y=a(x-h)^2+k[/tex]

Here, (h, k) are the vertex.

An engineer sketches a design for a flashlight that uses a mirror in the shape of a parabola to maximize the output of the light.

The function representing the mirror is graphed on the left. The graph for the parabola is attached below.

In the graph of parabola below, the vertex point of the parabola is at (6,2). Thus, the value of vertex points,

[tex]h=6\\k=2[/tex]

As the parabola has the y-intercept at y equal to 20. Thus, the equation of the parabola can be written as,

[tex]20=a(0-6)^2+2\\20-2=36a\\a=\dfrac{18}{36}\\a=\dfrac{1}{2}[/tex]

Put the values in the above equation as,

[tex]y=\dfrac{1}{2}(x-6)^2+2[/tex]

Thus, the function which models the mirror of flashlight, design by the engineer in the shape of parabola is,

[tex]y=\dfrac{1}{2}(x-6)^2+2[/tex]

Learn more about the vertex form of the parabola here;

https://brainly.com/question/17987697