Скачать или смотреть Exercise 3.1 Q1, Q2 Solved | Maximum/Minimum Value of Quadratic Functions | Class 11 Math New Book

Art of finding Maximum and Minimum values of Quadratic Functions!
Step-by-step solutions to Questions 1 and 2 from Exercise 3.1 in Chapter 3 of the Class 11 Mathematics (PTB) New Book 2025.
MathSolutions by Dr. Javaid Aly guides you through two essential techniques for analyzing quadratic functions:
(i) The algebraic method of Completing the Square
(ii) The graphical method of Sketching Parabolas.
📚 In This Video, You Will Learn:
✅ Question 1 (All Parts): How to find the Extreme Values (Max/Min) of quadratic functions by Completing the Square.
• Covers functions like f(x)=x^2+6x+13, f(x)=−x^2+8x+13, and more with positive and negative coefficients.
• Learn the vertex form f(x)=a(x−h)^2+k and how to use it to determine maxima and minima.
✅ Question 2 (All Parts): How to find the Extreme Point, Domain, and Range by Sketching the Graph.
• Step-by-step process: finding the vertex, y-intercept, x-intercepts, and sketching the parabola.
• Determine the Domain & Range of each function from its graph.
• Covers functions like f(x)=x^2−4x, f(x)=x^2−5x+6 and f(x)=6−x−x^2.
🔍 Special Highlights:
• Based on the latest PTB syllabus (2025), perfect for Punjab, Federal, and KPK Board students.
• Clear explanations of how the sign of a (the coefficient of x^2) determines whether the parabola opens upwards (minimum) or downwards (maximum).
• Essential for building a strong foundation for Calculus and competitive exams like ECAT, NUST, and FAST.
📖 Relevant Exercise: Class 11 Math, Chapter 3: Exercise 3.1 (Questions 1 & 2).
💡 Pro Tip: Keep a notebook handy! Pause the video after each problem and try to solve it yourself first for the best learning experience.
👍 If this video helps you, please LIKE, SHARE with your classmates, and SUBSCRIBE to @MATHSOL-1 for more! Turn on notifications 🔔 so you never miss an update.
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MathSolutions by Dr. Javaid Aly
Making Complex Mathematics Simple!
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