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Parabola Inequalities

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January 2, 2009
conicsparabolainequalitiesanalytic geometrygeometryspecial factorizations

Problem Statement

Let f(x)\equal{}x^2\plus{}6x\plus{}1, and let R R denote the set of points (x,y) (x,y) in the coordinate plane such that f(x)\plus{}f(y)\le0\text{ and }f(x)\minus{}f(y)\le0 The area of R R is closest to <spanclass=′latex−bold′>(A)</span> 21<spanclass=′latex−bold′>(B)</span> 22<spanclass=′latex−bold′>(C)</span> 23<spanclass=′latex−bold′>(D)</span> 24<spanclass=′latex−bold′>(E)</span> 25 <span class='latex-bold'>(A)</span>\ 21 \qquad <span class='latex-bold'>(B)</span>\ 22 \qquad <span class='latex-bold'>(C)</span>\ 23 \qquad <span class='latex-bold'>(D)</span>\ 24 \qquad <span class='latex-bold'>(E)</span>\ 25
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