The given quadratic equation has a vertex at (1, -1), indicating a maximum point due to the negative coefficient of the squared term. The x-intercepts are found at (2, 0) and (-1, 0), while the y-intercept is located at (0, -2). The axis of symmetry is defined by x = 1.
Vertex:
The vertex is at the point (1, -1).
Nature of the Vertex:
Since the coefficient of the squared term is -1 (negative), the vertex represents a maximum.
X-Intercepts:
To find x-intercepts, solve 2x - x^2 - 2 = 0.
Solutions are x = 2 and x = -1.
X-intercepts are at (2, 0) and (-1, 0).
Y-Intercept:
Substitute x = 0 into the equation to find f(0) = -2.
Y-intercept is at (0, -2).
Axis of Symmetry:
Use the formula x = -b/(2a) with a = -1 and b = 2.
The axis of symmetry is x = 1.