Question

Please help with question below

Answer 1

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`

is equivalent to this

`f(\text{x}) = 2(\text{x}-4)^2+2`

because the two negatives cancel to form a positive.

Compare it to the vertex form equation

`f(\text{x}) = a(\text{x}-h)^2+k`

to see that

• a = 2
• h = 4
• k = 2

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