Answer: Choice B) |x-2| - 6
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Step-by-step explanation:
Recall that for y = a| x-h | + k, the vertex is (h,k).
Since all of the answer choices have a > 0, this means all of the vertexes are the lowest point for each absolute value graph.
Consequently it tells us the lowest possible y value.
- For choice A, the smallest y output possible is y = 2
- For choice B, it would be y = -6
- For choice C, y = 6 is the lowest
- And choice D says y = -2 is the lowest y value
Choices A, C and D indicate that getting y = -5 is impossible. For instance, if y = 2 is the smallest, then there's no way to get y = -5. I recommend making a number line.
The only thing left is choice B. If we plug in y = -5 then we get...
y = |x-2| - 6
-5 = |x-2| - 6
-5+6 = |x-2|
|x-2| = 1
x-2 = 1 or x-2 = -1
x = 1+2 or x = -1+2
x = 3 or x = 1
Plugging either of those x values into y = |x-2| - 6 leads to y = -5
You could try solving something like -5 = |x-6| + 2 for x, but you'll find that it has no solutions.
As another alternative, you can graph each answer choice. Then see which one intersects the horizontal line y = -5. You should see that only y = |x-2| - 6 does so.