Answer:
c) x = 1 ; (1,5)
Explanation:
Axis of symmetry: x = -b / (2a)
Vertex: (h, k), where h = -b / (2a) and k = f(h)
Let's break down the steps to find the axis of symmetry and the vertex:
1. Identify the coefficients of the quadratic equation. In this case, a = -1 and b = 2.
2. Use the formula for the axis of symmetry to find the x-coordinate. Substitute the values of a and b into the formula: x = -2 / (2 * -1) = -2 / -2 = 1.
3. To find the y-coordinate (k) of the vertex, substitute the x-coordinate (h) into the function f(x). Plug in x = 1 into the function: f(1) = -(1)^2 + 2(1) + 4 = -1 + 2 + 4 = 5.
4. The axis of symmetry is x = 1, and the vertex is (1, 5).