Final answer:
To graph f(x) = 3(x + 1)² – 3, identify the vertex (-1, -3) and axis of symmetry x = -1. The function increases on the interval (-∞, -1) and decreases on the interval (-1, +∞).
Step-by-step explanation:
To graph the function f(x) = 3(x + 1)² – 3, we can start by identifying its vertex and axis of symmetry. This function is in the form of a parabola with a vertex form y = a(x - h)² + k, where (h,k) is the vertex and x = h is the axis of symmetry.
For the given function, the vertex is (-1, -3) as it's evident from the transformation of the standard x² parabola moved 1 unit left (due to +1 inside the brackets) and 3 units down (due to – 3 outside). The axis of symmetry is therefore the line x = -1.
The function is increasing on the interval (-∞, -1) and decreasing on the interval (-1, +∞), which is typical for a parabola that opens upwards (because the coefficient of (x + 1)² is positive).