Select the correct answer.The vertex of a parabola is at the point (3.1), and its focus is at (3.5), what function does the graph represent?A. f(x) = 1/16(x - 3)² - 1B. f(x) = 1/4(x + 3)² - 1C. f(x) = 1/4(x - 3)² - 1D. f(x) = 1/16(x - 3)² + 1​

Answer:[tex]y = \frac{1}{16} (x - 3)^{2} + 1[/tex]Step-by-step explanation:The vertex of the parabola is at the point (3,1) and its focus is at (3,5). Therefore, the axis of the parabola is x = 3 and the direction is positive y-axis. {Since focus is above the vertex.} Therefore, the equation of the parabola can be written as  (x - 3)² = 4a(y - 1) Where, a is the length between vertex and the focus which is (5 - 1) = 4 {Length is measured along x = 3 line} So, the final equation of the parabola is (x - 3)² = 4 × 4(y - 1) = 16(y -1) Now, rearranging the equation we get, [tex]y = \frac{1}{16} (x - 3)^{2} + 1[/tex] Therefore, option D is correct. (Answer)