Answer:
A) stretch, shift along the y–axis, and shift along the x–axis.
Step-by-step explanation:
Given the parent quadratic function, f(x) = x², and the transformed function in vertex form, g(x) = 2(x - 1)² + 2:
In the vertex form, g(x) = a(x - h)² + k
where:
(h, k) = vertex
a = makes the parent function wider (0 < a < 1) or narrower (a > 1).
h = determines the horizontal translation of the parent graph:
→ Horizontal translation of h units to the right: g(x) = f(x - h), where h > 0
→ Horizontal translation of |h| units to the left: g(x) = f(x - h), where h < 0.
k = determines the vertical translation of the parent graph.
Given these definitions, it is evident that the transformed function is narrower (vertical stretch by a factor of a = 2); shifted along the y-axis (with k = 2), and horizontally shifted along the x-axis given h = 1.
Therefore, the correct answer is Option A): stretch, shift along the y–axis, and shift along the x–axis.
