Page 15 - Mathematics Class - X

Unit 2 Algebra
Algebra

ACTIVITY 2.1

OBJECTIVE
To draw the graph of a quadratic polynomial and observe:
(i) The shape of the curve when the coefficient of x is positive.
2
(ii) The shape of the curve when the coefficient of x is negative.
2
(iii) Its number of zeroes.

MATERIALS REQUIRED
Cardboard Ruler Eraser Adhesive
Graph paper Pencil Pen

PRE-REQUISITE KNOWLEDGE
1. Concept of quadratic polynomial
2. Graph of quadratic polynomial

THEORY

1. Quadratic polynomial: A polynomial of the form ax + bx + c, a ≠ 0, where a, b and c are constants.
2
2. A real number a is said to be a zero of a quadratic polynomial, ax + bx + c, where a ≠ 0 if
2
aa + ba + c = 0. Any quadratic polynomial can have at most two zeroes.
2
3. For any quadratic polynomial ax + bx + c, a ≠ 0, the graph will be of two shapes either open upwards
2
like ∪ or open downwards like ∩ depending on whether a > 0 or a < 0, (these curves ∩ or ∪ are called
parabolas). This graph can cut the X-axis at most on two points because it can have at most two zeros.

PROCEDURE

1. Paste a graph paper on the cardboard.
2. Consider a quadratic polynomial; f (x) = ax + bx + c, where a ≠ 0.
2
3. For the equation, two cases arise:
(i) a > 0 (ii) a < 0

4. Now find the ordered pairs (x, f (x)) for different values of x.

x x x x ...................... x
1 2 3 n
f(x) f(x ) f(x ) f(x ) ...................... f(x )
1 2 3 n

5. Draw the above pairs in the Cartesian plane on the graph paper.

13