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Suppose p(x)=ax^2+bx+c is a quadratic polynomial satisfying p(7)−p(3)=214. Determine the value of p(9)−p(1).

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p(7) - p(3) = 214
49a + 7b + c - (9a + 3b + c) = 214
40a + 4b = 214

p(9) - p(1)
= 81a + 9b + c - (a+b+c0
= 80a + 8b
= 2(40a + 4b)
= 2(214)= 428

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