【京大2005】放物線と "線分" が交わる条件【方程式・領域】

⭐️ "Oshiemath" - Ask Hayashi questions as many times as you like for a fixed monthly fee. Try asking a question for free once! https://oshiemath.com/ ⭐️ "Hayashi Math Classroom" - A specialized math cram school where you can receive direct instruction from Hayashi. Please come for a trial lesson & consultation! https://hayashi-math.com/ ✅ Official LINE for students aiming for top universities: https://lin.ee/lI7n1SJ Registered members receive benefits & live sessions for exam takers. ℹ️ Hayashi Shunsuke's Profile https://hayashishunsuke.com/profile/ Eito Junior High School → Tsukuba University High School → University of Tokyo, Science I → University of Tokyo, Department of Physics Achieved 90% on the University of Tokyo's second-stage mathematics exam and passed on his first try. 2014 Japan Physics Olympiad Gold Medal 2014 University of Tokyo Mock Exam Physics 1st Place ℹ️ Important Notes Explanations are Hayashi Shunsuke's own and not official university explanations. We use Amazon Associate links for book and other product introductions. For students aiming for the top, we provide explanations of university entrance exam mathematics, focusing on national and public university entrance exam questions! Please subscribe to our channel. We've selected a problem related to regions from the 2005 Kyoto University entrance exam (common to both humanities and science students). This problem asks for the conditions for two coefficients such that a parabola and a line segment intersect, and then to illustrate this. If the conditions were for a parabola and a "line" to intersect, it would be easy, but the fact that it's interrupted makes it a bit tricky. At first glance, you might think, "Wow, this is complicated," but we'll tackle it by breaking it down into problems involving finding the maximum and minimum values ​​of quadratic functions and problems involving the arrangement of solutions. This type of problem frequently appears in difficult university entrance exams, regardless of whether you're in humanities or science, so be sure to be able to solve it! ---------- Table of Contents 00:00 2005 Kyoto University, Common Problem for Humanities and Sciences 00:42 Quadratic Equation Satisfied by the Coordinates of Intersection Points 02:24 Solution 1: Maximum and Minimum Values ​​of the Quadratic Function 04:17 Solution 1: Case Analysis for Maximum and Minimum Values 07:33 Solution 1: First Case 09:07 Solution 1: Second Case 11:05 Solution 1: Third Case 12:35 Solution 1: Fourth Case 14:02 Solution 1: Summarizing the Results for Each Case 15:49 Solution 1: Visualizing the Results 19:05 Summary of Solution 1 20:14 Let's Consider It 22:50 Solution 2: Arrangement of Solutions to the Quadratic Equation 24:23 Solution 2: Case distinctions based on axis position 30:13 Summary of Solution Method 2 31:08 Comparison of the two solution methods and points to note 32:02 Advice for learners 32:41 Conclusion