Question

Does anyone know how to do this?

Answer 1

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Answer:

1. h = -2; k = 0; vertex = (-2, 0)
2. h = 3; k = 0; vertex = (3, 0)

Step-by-step explanation:

Translation of a function to the right h units and up k units is accomplished by ...

  g(x) = f(x -h) +k

Here, we have f(x) = |x|, so the translation will be ...

  g(x) = |x -h| +k

or ...

  y = |x -h| +k

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The function y = |x| has its vertex at (0, 0), so translation by (h, k) moves the vertex to (0 +h, 0 +k) = (h, k).

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You will notice that the given equations you are given have no "+k" added on, so k = 0 in both cases. The value of h is the opposite of the constant between the absolute value bars.

1. y = |x +2|

  h = -2, k = 0

  vertex: (-2, 0)

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2. y = |x -3|

 h = 3, k = 0

  vertex: (3, 0)

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Additional comment

This is all about matching patterns. You need to be able to identify the variable (x) and what has been added or subtracted to/from it. You need to be able to identify the "parent" function (what you have with nothing added or subtracted), and determine if something is added or subtracted to to/from that. Here, the parent function is |x|. Nothing has been added to the function (outside the absolute value bars), but something has been added to x (inside the absolute value bars).