To find the coordinates for the function \( g(h) = -6h^2 - 2h + h \) with the given inputs of \( -8, -6, -4, -2, \) and \( 0 \), we will first simplify the function:
\[ g(h) = -6h^2 - 2h + h = -6h^2 - h \]
Now, we will calculate \( g(h) \) for each input:
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Input: \( h = -8 \) \[ g(-8) = -6(-8)^2 - (-8) = -6 \cdot 64 + 8 = -384 + 8 = -376 \] Coordinate: \( (-376, -8) \)
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Input: \( h = -6 \) \[ g(-6) = -6(-6)^2 - (-6) = -6 \cdot 36 + 6 = -216 + 6 = -210 \] Coordinate: \( (-210, -6) \)
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Input: \( h = -4 \) \[ g(-4) = -6(-4)^2 - (-4) = -6 \cdot 16 + 4 = -96 + 4 = -92 \] Coordinate: \( (-92, -4) \)
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Input: \( h = -2 \) \[ g(-2) = -6(-2)^2 - (-2) = -6 \cdot 4 + 2 = -24 + 2 = -22 \] Coordinate: \( (-22, -2) \)
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Input: \( h = 0 \) \[ g(0) = -6(0)^2 - (0) = 0 \] Coordinate: \( (0, 0) \)
Thus, the resulting coordinates are:
- \( (-376, -8) \)
- \( (-210, -6) \)
- \( (-92, -4) \)
- \( (-22, -2) \)
- \( (0, 0) \)
From the options given, the closest match is:
- \( (-8, -376), (-6, -210), (-4, -92), (-2, -22), (0, 0) \)
So, the correct selection is: (−8, −376), (−6, −210), (−4, −92), (−2, −22), (0, 0).