Question

If f(x) = ax2 + bx + c is a quadratic polynomial such that f(0) = 0 and f(1) = 1. Prove that, f(x) = ax2 + (1 – a)x.

Answer 1

f(x) = ax2 + bx + c
f(0) = a(0)2 + b. 0 + c
f(0) = c = 0
Therefore, c = 0
Now, f(x) = ax2 + bx
Also,
f(1) = 1
a(1)2 + b. 1 = 1
a + b = 1
b = (1 – a)
f(x) = ax2 + (1 – a)x.

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Answer 2

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