CBSE Class 10 Maths Lab Activity - Draw Quadratic Polynomial and Observe
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.
STEPS OF CONSTRUCTION
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.
5. Plot these ordered pairs in the cartesian plane
6. Join the plotted points by a free hand curve. Based on polynomial used, you may have graphs as shown in following figures:
DEMONSTRATION
1. The shape of the curve obtained in each case is a parabola.
2. Parabola opens upward when coefficient of x² is positive.
3. It opens downward when coefficient of x² is negative.
4. Maximum number of zeroes which a quadratic polynomial can have is 2.
OBSERVATION
1. Parabola in Fig. 1 opens ______
2. Parabola in Fig. 2 opens _______
3. In Fig. 1, parabola intersects x-axis at ______ point(s).
4. Number of zeroes of the given polynomial is ________.
5. Parabola in Fig. 2 intersects x-axis at ______ point(s).
6. Number of zeroes of the given polynomial is ______.
7. Parabola in Fig.3 intersects x-axis at ______ point(s).
8. Number of zeroes of the given polynomial is _______.
9. Maximum number of zeroes which a quadratic polynomial can have is __________.
APPLICATION
This activity helps in:
1. understanding the geometrical representation of a quadratic polynomial
2. finding the number of zeroes of a quadratic polynomial
A Sample project is shown here.
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