Problem

Compare \(f(x)=|x+4|-2\) and \(g(x)=-|x+4|-2\) through their vertex-form parameters. State their shared vertex, axis, and width, identify the changed parameter, and explain the opening directions and exact reflection relationship.

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Both differ by a reflection, so one opens up and one opens down. This does not identify their common vertex, axis, or width.

Both have vertex (−4, −2), axis x = −4, and the same width. The negative factor reflects g across y = −2, so f opens up and g opens down.

Both have vertex (−4, −2), but g is reflected horizontally across x = −4. The negative factor is outside the absolute value, so it reflects vertically across y = −2.

Both have vertex (4, −2) and axis x = 4, while g opens down. The expression x + 4 shifts the vertex to x = −4, not x = 4.

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Compare \(f(x)=|x+4|-2\) and \(g(x)=-|x+4|-2\) through their vertex-form parameters. State their shared vertex, axis, and width, identify the changed parameter, and explain the opening directions and exact reflection relationship.

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