In Problems 45–60,

(a) Find the vertex and the axis of symmetry of each quadratic function, and determine whether the graph is concave up or concave down.

(b) Find the y-intercept and the x-intercepts, if any.

(c) Use parts (a) and (b) to graph the function.

(d) Find the domain and the range of the quadratic function.

(e) Determine where the quadratic function is increasing and where it is decreasing.

(f) Determine where f (x) > 0 and where f (x) < 0.

f (x) = −3x² + 3x − 2