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Final Answer:
The graphs should be parabolas opening upward (since a = 1 > 0), with vertices at:
1. (3, −5) for $ y = x^2 - 6x + 4 $
2. (−1, −6) for $ y = x^2 + 2x - 5 $
3. (0, −3) for $ y = x^2 - 3 $
4. (−3, −8) for $ y = x^2 + 6x + 1 $

Each graph passes through points found by plugging in x-values (e.g., for #1: x = 0 → y = 4; x = 1 → y = −1; x = 2 → y = −4; x = 3 → y = −5; x = 4 → y = −4; x = 5 → y = −1; x = 6 → y = 4), forming a symmetric U-shape around the vertex.