Maths Olympiad Prep

Track / Stage 4 / 262 of 340 #522 of 1964

Problem 522

AMC 12 late, AIME early
Algebra Difficulty 4.9 Find the answer

Given the sets P={y∣y=x2+3x+1,x∈R},Q={y∣y=−x2−3x+1P=\left\{y \mid y=x^{2}+3 x+1, x \in \mathbf{R}\right\}, Q=\left\{y \mid y=-x^{2}-3 x+1\right., x∈R}x \in \mathbf{R}\}, find P∩QP \cap Q.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Next problem →

Official solution

 (7) P∩Q=[−54,134]\begin{array}{l}\text { (7) } P \cap Q= \\ {\left[-\frac{5}{4}, \frac{13}{4}\right]}\end{array}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.