CAT 2022 Linear and Quadratic Equations Question (Medium)

Question

Let be a quadratic polynomial in such that for all real numbers . If and , then is equal to

Accepted Answer

Step 1 Given quadratic function Step 2 Condition parabola opens upwards and vertex lies on or above x-axis Step 3 Given symmetry at axis of symmetry is Thus, Step 4 Given points and Step 5 Use ... i Step 6 Use ... ii Step 7 Solve equations From i Sub into ii Then Step 8 Function Step 9 Find

CAT 2022

Quantitative

Linear and Quadratic Equations

Medium

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

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