Question

Given f(x)² = x² and g(x) = (x+6)² + 2. List the transformations of g(x).

Answer 1

The function g(x) = (x+6)² + 2 represents a quadratic function. The transformations of g(x) include an upward shift of 2 units, a horizontal shift of 6 units to the left, and no change in the shape or orientation of the parabola.

Step-by-step explanation:

The given function g(x) = (x+6)² + 2 represents a quadratic function. To identify the transformations of g(x), we can compare it to the standard form of a quadratic function y = a(x-h)² + k.

1. The coefficient 'a' determines the direction and scale of the parabola. In this case, a = 1, so the parabola opens upwards.
2. The values of 'h' and 'k' determine the vertex of the parabola. In this case, (h, k) = (-6, 2), so the vertex is located at (-6, 2).
3. Lastly, the '+6' inside the parentheses represents a horizontal shift of 6 units to the left.

Therefore, the transformations of g(x) are: an upward shift of 2 units, a horizontal shift of 6 units to the left, and no change in the shape or orientation of the parabola.