Mathematics Lab Activity-01 Class 10 | Quadratic Polynomial

   Mathematics Lab Activity-01 Class X

Mathematics Laboratory Activities on Quadratic Polynomial for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 02 : quadratic polynomial

Activity - 01

Objective

To draw the graph of a quadratic polynomial and observe:

(i) The shape of the curve when the coefficient of x² is positive.

(ii) The shape of the curve when the coefficient of x²  is negative.

(iii) Its number of zeroes.

MATERIAL REQUIRED

Cardboard, graph paper, ruler, pencil, eraser, pen, adhesive.

Procedure

1. Take cardboard of a convenient size and paste a graph paper on it.

2. Consider a quadratic polynomial f (x) = ax² + bx + c.

3. Two cases arise: (i) a > 0   (ii) a < 0

4. Find the ordered pairs (x, f (x)) for different values of x in the quadratic equation x² + 0x - 1 (any other quadratic equation can be taken with a > 0).

5. Plot these ordered pairs in the cartesian plane.

6. Join the plotted points by a free hand curve as shown in the figure 1.

Figure 1

7. Find the ordered pairs (x, f (x)) for different values of x in the quadratic equation -x² + 0x + 4 (any other quadratic equation can be taken with a < 0).

8. Plot these ordered pairs in the cartesian plane.

9. Join the plotted points by a free hand curve as shown in the figure 2.

Figure 2

10. The shape of the curve obtained in each case (in fig.1 and in fig. 2) is a parabola.

11. It opens upward when coefficient of x²  is positive [see Fig. 1]. 

12. Parabola opens downward when coefficient of x² is negative [see Fig. 2 ]

13. Maximum number of zeroes which a quadratic polynomial can have is 2, because in each case the curves cut the x-axis at two points.

OBSERVATION

1. Parabola in Fig. 1 opens  upward.
2. Parabola in Fig. 2 opens downward.
3. In Fig. 1, parabola intersects x-axis at two points.
4. Number of zeroes of the given polynomial are two.
5. Parabola in Fig. 2 intersects x-axis at two point(s).
6. Number of zeroes of the given polynomial are two.
7. Maximum number of zeroes, a quadratic polynomial can have = two.

APPLICATION

This activity helps in
1. Understanding the geometrical representation of a quadratic polynomial
2. Finding the number of zeroes of a quadratic polynomial.

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