Question

Which function represents the quadratic function f(x) = x2 after a vertical stretch by a factor of 2? A. g(x) = (x – 2)2 B. g(x) = x2 + 2 C. g(x) = 2x2 D. g(x) = (x – 2)2 + 2

Answer 1

The quadratic function f(x) = x^2, after a vertical stretch by a factor of 2, is represented by g(x) = 2x^2. The correct answer is C. g(x) = 2x2.

Step-by-step explanation:

The question concerns the transformation of a quadratic function involving a vertical stretch. The original function given is f(x) = x2.

When we apply a vertical stretch by a factor of 2, we are essentially multiplying the entire function by 2.

Thus, the transformed function, represented by g(x), would be g(x) = 2x2.

This scaling affects the 'a' coefficient in the standard quadratic function y = ax2, which results in a steeper parabola. Therefore, the correct answer is C. g(x) = 2x2.