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The quadratic equation problem. The real SMTE exam!

Anyone preparing for the 4th grade entrance exam, don't miss it. 🚀

📚 easy to understand summary + detailed solution.

Who wants to take the exam, must see 👏

# Tutor entrance exam 4 # SMTE # quadratic equation # The butler tutored math # Famous school entrance exam# math

2025/8/27 Edited to

ถ้าเตรียมสอบเข้า ม.4 (โดยเฉพาะแนว SMTE) “สมการกำลังสอง” มักออกได้หลายรูปแบบ ไม่ได้มีแค่แก้สมการให้ได้ x แต่ชอบผสมเรื่องกราฟ พื้นที่ และจุดตัดแกนด้วย เราเลยสรุปแนวทำโจทย์ที่เจอบ่อยแบบอ่านจบแล้วไปทำข้อสอบได้ทันที 1) เช็กลักษณะโจทย์ก่อนทำ (ช่วยลดพลาด) - โจทย์ให้สมการเป็นกราฟพาราโบลา เช่น y = 2x^2 - x - 3 แล้วถาม “ตัดแกน X ที่ไหน” หรือ “พื้นที่สามเหลี่ยมจากจุดตัดแกน” - โจทย์ให้เป็นสมการกำลังสองตรงๆ เช่น ax^2 + bx + c = 0 แล้วให้หาคำตอบ/เงื่อนไข ทริคคืออ่านคำว่า “ตัดแกน X” = ให้ y=0 และ “ตัดแกน Y” = ให้ x=0 2) วิธีหาจุดตัดแกน X (เจอประจำในข้อสอบม.4) เมื่อ y = 2x^2 - x - 3 ตั้ง y=0 จะได้ 2x^2 - x - 3 = 0 จากนั้นใช้แยกตัวประกอบ/สูตรกำลังสอง ข้อนี้แยกได้เป็น (2x-3)(x+1)=0 ดังนั้น x = 3/2 หรือ x = -1 จุดตัดแกน X คือ A(-1,0) และ B(3/2,0) 3) วิธีหาจุดตัดแกน Y ให้ x=0 แทนใน y = 2x^2 - x - 3 จะได้ y=-3 จุดตัดแกน Y คือ C(0,-3) 4) แนวโจทย์ยอดฮิต: พื้นที่สามเหลี่ยมจากจุดตัดแกน ถ้าโจทย์บอกว่า “กราฟตัดแกน X ที่ A,B และตัดแกน Y ที่ C พื้นที่ของรูปสามเหลี่ยม ABC เท่าไร” เราจะใช้สูตรพื้นที่สามเหลี่ยมจากพิกัด หรือมองเป็น “ฐาน × สูง ÷ 2” ก็ได้ (ง่ายกว่า) - ฐาน AB อยู่บนแกน X ความยาว = |xB - xA| = |3/2 - (-1)| = 5/2 - ความสูงคือระยะจาก C ไปถึงแกน X (เพราะฐานอยู่บนแกน X) = |yC| = 3 พื้นที่ = (5/2 × 3) ÷ 2 = 15/4 = 3.75 ตารางหน่วย 5) ถ้าอยากได้คะแนนชัวร์: เช็กลิสต์ก่อนส่งคำตอบ - จุดตัดแกน X ต้องมี y=0 เสมอ (อย่าเผลอใส่ y อื่น) - จุดตัดแกน Y ต้องมี x=0 เสมอ - พื้นที่ต้องเป็นค่าบวก และหน่วยมักเป็น “ตารางหน่วย” ลองเอาขั้นตอนนี้ไปไล่ทำ “โจทย์คณิตศาสตร์ง่ายๆ” แนวสมการกำลังสองหลายๆ ข้อ แล้วจะเริ่มเห็นแพทเทิร์นของข้อสอบเข้า ม.4 ชัดมาก ทำเร็วขึ้นและพลาดน้อยลงจริง

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solving quadratic equation using factor 🫶

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