Answer: Min value is 2 (choice B)
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Reasoning:
The given function
![f(\text{x}) = -2\left[-(\text{x}-4)^2\right]+2](https://img.qammunity.org/2023/formulas/mathematics/high-school/cm00ph8ih50k8ktmlnci2y91t7n84ozsgd.png)
is equivalent to this

because the two negatives cancel to form a positive.
Compare it to the vertex form equation

to see that
The (h,k) = (4,2) is the vertex. It is the highest point when a < 0.
Or the vertex is the lowest point when a > 0.
We have a = 2 as a positive number. Therefore, the vertex is the lowest point on the parabola.
The function f(x) minimizes at f(x) = 2 when x = 4
In other words, the input x = 4 produces the lowest output y = f(x) = 2. Any other inputs will make f(x) some value larger than 2.
The graph is below. It visually confirms the lowest point is when y = 2