Final answer:
The graph of the quadratic function f(x) = a(x - h)² + k is a parabola with its vertex at (h, k), opening upwards for a > 0 and downwards for a < 0. The value of 'a' affects the width of the parabola.
Step-by-step explanation:
The quadratic function f(x) = a(x - h)² + k represents a parabola. The graph of this function is a curved line that opens upwards if the value of a is positive, and downwards if the value of a is negative. The vertex of this parabola is at the point (h, k), which is the highest or lowest point of the graph depending on the sign of a. If a is greater than 1 or less than -1, the parabola will be narrower than the standard parabola y = x²; if a is between 0 and 1 or 0 and -1, the parabola will be wider.