Page 16 - Mathematics Class - X

6. Join the plotted points by a free hand curve as shown in figures.
Y Y Y

X′ X X′ X X′ X

Y′ Y′ Y′

Fig. (a) Fig. (b) Fig. (c)

OBSERVATIONS

1. Parabola in Fig. (a) opens ________ .

2. Parabola in Fig. (b) opens ________ .

3. In Fig. (a), parabola intersects X-axis at ________ points(s).

4. In Fig. (a), number of zeroes of the given polynomial is ________ .

5. Parabola in Fig. (b) intersects X-axis at ________ points(s).

6. Parabola in Fig. (c) intersects X-axis at ________ points(s).

7. Number of zeroes of the given polynomial is ________ .
8. Maximum number of zeroes which a quadratic polynomial can have, is ________ .

INFERENCE

1. The shape of the curve obtained in each case is a parabola.

2. Parabola opens upward when coefficient of x is positive (Figs. (b) and (c)).
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3. It opens downward when coefficient of x is negative (Fig. (a)).
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4. Maximum number of zeroes which a quadratic polynomial can have is 2.

EXTENDED TASK
Using this activity, draw the graphs of the following polynomials.

1. f (x) = x – 2x – 8
2
2. f (x) = x – 4
2
3. Find the number of zeroes of a quadratic polynomial.

APPLICATION
This activity helps to understand the geometrical representation of a quadratic polynomial.

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