• 要求ようきゅう — demand
• 求職きゅうしょく — job hunting
• 求人きゅうじん — job offer
• 請求せいきゅう — request (invoice, bill)
• 探求たんきゅう — quest, inquiry
• 求もとめる — to seek, request

The character 求 is derived from a pictograph representing a hand grasping fur or cloth, symbolizing the act of reaching for or seeking something. Over time, it came to mean "to request" or "to desire." It also serves as the phonetic base in many compound kanji.

助たすけを 求もとめた。
I asked for help.

彼かれは 新あたらしい 仕事しごとを 求もとめています。
He is looking for a new job.

キュウ is used in compounds such as 要求 and 探求. The kun-yomi もとめる is used for more everyday expressions like 愛を求める (seek love) or 助けを求める (seek help).