Final answer:
The modification from f(x) = 2x² to g(x) = 3x² makes the parabola narrower and steeper, as the coefficient before x² determines the rate of growth and width of the curve.
Step-by-step explanation:
The modification from f(x) = 2x² to g(x) = 3x² changes the parabola by altering its width and the rate at which it grows. To understand this, consider that the coefficient of x² in a quadratic equation like y = ax² affects the parabola's steepness and width. In the case of f(x), the coefficient is 2, which means the parabola opens upward and is relatively wide. For g(x), the coefficient has increased to 3, which makes the parabola open upward as well but with a steeper curve and narrower shape compared to f(x).
This is because a larger coefficient in front of x² means the value of y increases more rapidly as x moves away from zero, resulting in a graph that is steeper and less spread out. This can also be thought of in terms of the parabola's vertex remaining unchanged at the origin, but with the sides of the parabola being pulled inwards, making it narrower.