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Quadratic function maximum value

CAT 2007 Slot 1 · Quantitative Ability · Easy · Functions

This is an easy Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A quadratic function f(x)f(x) attains a maximum of 3 at x=1x = 1. The value of the function at x=0x = 0 is 1. What is the value f(x)f(x) at x=10x = 10?

  1. A.

    -119

  2. B.

    -159

  3. C.

    -110

  4. D.

    -180

  5. E.

    -105

Answer

B

Explanation

Vertex form: f(x)=a(x−1)2+3f(x) = a(x - 1)^2 + 3. Since f(0)=1  ⟹  a(0−1)2+3=1  ⟹  a=−2f(0) = 1 \implies a(0 - 1)^2 + 3 = 1 \implies a = -2. So f(x)=−2(x−1)2+3f(x) = -2(x - 1)^2 + 3. At x=10x = 10: f(10)=−2(9)2+3=−162+3=−159f(10) = -2(9)^2 + 3 = -162 + 3 = -159.

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