CAT 2022 Slot 2 QA Q20 Functions & Graphs

Question 20 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

Let \(f(x)\) be a quadratic polynomial in \(x\) such that \(f(x) \geq 0\) for all real numbers \(x\). If \(f(2)=0\) and \(f(4)=6\), then \(f(-2)\) is equal to
  1. A
    12
  2. B
    36
  3. C
    24
  4. D
    6

Answer: (C) 24 Functions & Graphs MCQ

Solution

  1. A quadratic that is never negative and has a root at 2 must touch the axis there: \(f(x)=k(x-2)^2\).
  2. \(f(4)=4k=6\Rightarrow k=1.5\).
  3. \(f(-2)=1.5\times16=24\).

Same concept in other years

See every question on Minimum or maximum of a quadratic at its vertex.

More Functions & Graphs questions from CAT

All 23 Functions & Graphs questions asked since 2017.