Final answer:
The statement which describes the non-rigid transformation in the function y+ 5 = − 2(x − 1)²/2 is The graph is shifted 5 units down.
The answer is option ⇒B
Step-by-step explanation:
The correct answer is B. The graph is shifted 5 units down.
To understand the non-rigid transformation in the given function y + 5 = -2(x - 1)²/2, let's analyze the equation.
The general form of a quadratic function is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
In this case, the equation y + 5 = -2(x - 1)²/2 can be rewritten as y = -2(x - 1)²/2 - 5.
By comparing this equation with the general form, we can see that the vertex of the parabola is at (1, -5).
Now, to determine the non-rigid transformation, we compare the vertex (1, -5) with the standard vertex (h, k) = (0, 0).
To shift the graph from the standard vertex (0, 0) to the vertex (1, -5), we need to perform the following transformations:
- 1. Shift 1 unit to the right: This means the graph is shifted horizontally by 1 unit to the right.
- 2. Shift 5 units down: This means the graph is shifted vertically by 5 units downwards.
Therefore, the non-rigid transformation in the given function is that the graph is shifted 5 units down, which corresponds to answer choice B.