Question

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

Answer 1

a

Explanation:

Answer 2

Option A. is the answer.

Explanation:

In the given sketch the function represents a parabola.

Which is in the form of f(x) = a(x - h)²+ k , function in a vertex form..

Since graph opens above means a > 0.

Vertex of the given parabola is (6, 2), Therefore equation will be

y = a(x - 6)² + 2

Since parabola has y-intercept as y = 20

Now by putting (0, 20) in the equation equation we can get the value of a.

20 = a(0 - 6)² + 2

20 = 36a + 2

36a = 20 - 2 = 18

a = 18/36 = 1/2

The final function will be in the form of

`f(x)=(1)/(2)(x-6)^(2)+2`

Therefore option A. is the answer.