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Which one of the following is the second degree polynomial function f(x) where f(0) = 5, f(-1) = 10 and f(1) = 6?

Which one of the following is the second degree polynomial function f(x) where f(0) = 5, f(-1) = 10 and f(1) = 6? Correct Answer 3x<sup>2</sup> - 2x + 5

Concept:

General form of a second degree polynomial function is: P (x) = a0 + a1 × x + a2 × x2, where a0, a1 and a2 are real coefficients and a2 ≠ 0.

Calculation

As we know that, general form of a second degree polynomial function is: P (x) = a0 + a1 × x + a2 × x2, where a0, a1 and a2 are real coefficients and a2 ≠ 0.

Let f(x) = a × x2 + b × x + c where a, b and c are real coefficients and a ≠ 0.

Given: f(0) = 5, f(-1) = 10 and f(1) = 6.

⇒ f(0) = c = 5

⇒ f(- 1) = a - b + 5 = 10          ----(1)

⇒ f(1) = a + b + 5 = 6          ---(2)

By adding (1) and (2), we get

⇒ 2a + 10 = 16 ⇒ a = 3.

Now by substituting a = 3 in equation (1) we get,

⇒ 3 - b + 5 = 10 ⇒ b = - 2.

Hence, f(x) = a × x2 + b × x + c = 3x2 - 2x + 5.

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