NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 2: Polynomials - Exercise 2.1

Question 11

Step 1: Recall the property of quadratic graphs.

The graph of a quadratic polynomial \(ax^2 + bx + c\) is always a parabola.

A parabola is a smooth U-shaped curve that opens either upwards (if \(a > 0\)) or downwards (if \(a < 0\)).

Important: A quadratic polynomial graph can have only one turning point, called its vertex.

Step 2: Check each option.

Option (A): The graph is a parabola opening upwards. Valid quadratic graph.

Option (B): The graph is a parabola opening downwards. Valid quadratic graph.

Option (C): The graph is also a parabola opening downwards. Valid quadratic graph.

Option (D): The curve bends twice, showing two turning points. ❌ This is not possible for a quadratic polynomial, but it is possible for a cubic polynomial.

Conclusion: The graph in option (D) is not the graph of a quadratic polynomial.

Correct answer: (D).