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:Option A. is the answer.Step-by-step 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 + 2Since parabola has y-intercept as y = 20Now by putting (0, 20) in the equation equation we can get the value of a.20 = a(0 - 6)² + 220 = 36a + 236a = 20 - 2 = 18a = 18/36 = 1/2The final function will be in the form of [tex]f(x)=\frac{1}{2}(x-6)^{2}+2[/tex]Therefore option A. is the answer.