Find the quadratic polynomial f(x) such that f(0) = 3, f(1) = -5, and f(2) = 7.
+526 Let f(x) = ax2 + bx + c
⇒f(0) = c = 3
f(1) = a + b + c = -5
⇒ a + b = -8
f(2) = 4a + 2b + c = 7
⇒ 4a + 2b = 4 ⇒ 2a + b = 2
⇒ 2a + b - a - b = 2 + 8
a = 10
b = -18
f(x) = 10x2 - 18x + 3
