To determine which ordered pair is on the graph of the equation \( y = x^2 + 2 \), we can substitute the \( x \)-value from each option into the equation and see if the resulting \( y \)-value matches the \( y \)-value from the ordered pair.
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Option A: (5, 49) \[ y = 5^2 + 2 = 25 + 2 = 27 \] This does not match \( y = 49 \).
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Option B: (4, 10) \[ y = 4^2 + 2 = 16 + 2 = 18 \] This does not match \( y = 10 \).
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Option C: (-1, 1) \[ y = (-1)^2 + 2 = 1 + 2 = 3 \] This does not match \( y = 1 \).
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Option D: (-6, 38) \[ y = (-6)^2 + 2 = 36 + 2 = 38 \] This matches \( y = 38 \).
From the evaluations above, the only ordered pair that lies on the graph of the equation \( y = x^2 + 2 \) is option D: (-6, 38).
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