Best unit 3 theory of quadratic functions solved notes class 11 punjab boards – 100% solved exercises with easy step-by-step solutions, graphs, diagrams & marking scheme from new book (PECTAA, Punjab Curriculum and Textbook Board, Ali Brothers, Ilmi Kitab Khana, Scholar Publications, Caravan Book House, Farhan Publishers).
Perfect for Punjab boards exams 2026 – score 90+ marks! Ideal for students, teachers & lecturers in renowned registered institutions from all 9 boards like Aitchison College Lahore (Lahore Board), Sadiq Public School Bahawalpur (Bahawalpur Board), Army Public Schools (Rawalpindi & Multan Boards), Beaconhouse Schools (Faisalabad & Gujranwala Boards), Forman Christian College Lahore (Lahore Board), Government College University Faisalabad (Faisalabad Board), Cadet College Hasan Abdal (Rawalpindi Board), Cadet College Petaro (near Multan Board), Cadet College Okara (Sahiwal Board), Cadet College Kohat (registered with Punjab boards), Cadet College Sargodha (Sargodha Board), Cadet College Jhang (Faisalabad Board), Cadet College Pasrur (Gujranwala Board), Cadet College Spinkai (DG Khan Board), Military College Jhelum (Rawalpindi Board), Garrison Cadet College Kohat, and many more.
Exercise 3.1 – Max/Min by Completing Square (All Questions Solved) Exercise 3.1 Page 72 Full Solutions ↳ Exercise 3.1 Complete Solved PDF ↳ Q1(i) f(x)=x²+6x+13 = (x+3)²+4, Min 4 at x=-3 ↳ Q1(ii) f(x)=x²+4x = (x+2)²-4, Min -4 at x=-2 ↳ Q1(iii) f(x)=-x²+8x+13 = -(x-4)²+29, Max 29 at x=4 ↳ Q1(iv) f(x)=-x²-3x-5 = -(x+3/2)²-11/4, Max -11/4 at x=-3/2 ↳ Q1(v) f(x)=3x²+6x-13 = 3(x+1)²-16, Min -16 at x=-1 ↳ Q1(vi) f(x)=-2x²-x+21 = -2(x+1/4)²+169/8, Max 169/8 at x=-1/4
All Remaining Exercises + Review Exercise (100% Solved) ↳ Exercise 3.2 Quadratic Equations Solved ↳ Exercise 3.3 Roots & Coefficients ↳ Exercise 3.4 Discriminant & Nature ↳ Exercise 3.5 Applications & Word Problems ↳ Review Exercise Unit 3 Full Solved
Bonus Resources ↳ Quadratic Functions Formulas Cheat Sheet PDF ↳ Top 30 Completing Square Shortcuts ↳ Quadratic Functions Video Series ↳ Unit 3 Past Papers Solved (2018-2025) ↳ Unit 2 Functions Graphs Notes ↳ Unit 4 Matrices Determinants Coming Soon
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External Links
- PCTB Official → pctb.punjab.gov.pk
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