Page 43 - Mathematics Class - XI

5. Take one more wire and fix it in such a way that it passes through the points where straight wire meet the
x-axis and the wire takes the shape of a curve (parabola) as shown in Fig. (b).

Fig. (b)
DEMONSTRATION

1. The wire through the points A and B represents the straight line given by y = x – a, intersecting the x-axis
and y-axis at (a, 0) and (0, –a) respectively.
2. The wire through the points C and D represents the straight line given by y = x – b, intersecting the x-axis
and y-axis at (b, 0) and (0, –b) respectively.

OBSERVATION
1. The line given by the linear function y = x – a intersects the axes at the point A and B whose coordinates are
(a, 0) and (0, –a).
2. The line given by the linear function y = x – b intersects the axes at the point C and D whose coordinates are
(b, 0) and (0, –b).

3. The curve passing through A and C is given by the function y = k(x – a) (x – b) where a, b > 0, which is a
parabolic function.

CONCLUSION

This activity concludes that the quadratic equation has two zeroes which represent the linear functions and linear
functions represent the graph of straight lines.

APPLICATION

This activity is used to find the zeroes and the shape of a graph of a quadratic polynomial.

Knowledge Booster
−+b D −−b D
The quadratic equation ax + bx + c = 0 with real coefficients has two roots given by and ,
2
2 a 2 a
where D = b – 4ac, called the discriminant of the equation.
2
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