Question

Compare the shapes of the parabolas of y = x^2 and y = 3x^2. More specifically, why does the parabola of y = 3x^2 appear to be "skinnier"?

A. The parabola of y = 3x^2 is skinnier because it has a larger coefficient of x^2.
B. The parabola of y = x^2 is skinnier because it has a larger coefficient of x^2.
C. The parabolas of y = x^2 and y = 3x^2 have the same shape.
D. The shape of the parabola is unrelated to the coefficient of x^2.

Answer 1

The parabola of y = 3x^2 is 'skinnier' than that of y = x^2 because the larger coefficient of x^2 in the equation causes the graph of the parabola to rise more quickly, thus appearing narrower.

Step-by-step explanation:

When comparing the shapes of the parabolas of y = x^2 and y = 3x^2, we are looking at how the coefficient of x^2 affects the width of the parabola. For the equation y = x^2, the coefficient is 1, which gives it a certain width. However, when looking at the equation y = 3x^2, the coefficient is larger - it is 3.
This larger coefficient causes the parabola to be 'skinnier.' The reason is that for any given value of x, the value of y is tripled compared to the y = x^2 parabola, which means the graph will rise more quickly and thus appear narrower. Therefore, the correct answer is A: The parabola of y = 3x^2 is skinnier because it has a larger coefficient of x^2.