ACTIVITY - 4
: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
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The Graph of a Quadratic Polynomial and its observations are as follows:
- Let us consider a quadratic equation for example,
- x² + 2x + 4 = 0 and -x² + 2x + 4 = 0
- i) The shape of the curve when the coefficient of x2 is positive
- x² + 2x + 4 = 0
- x = -1 + √3 i , -1 - √3 i
- The shape of the curve is upward opening parabolic curve.
- ii) The shape of the curve when the coefficient of x2 is negative
- x² + 2x + 4 = 0
- x = 1 - √5 , 1 + √5
- The shape of the curve is downward opening parabolic curve.
- iii) The shape of the curve when the coefficient of x2 is zero
- 0² + 2x + 4 = 0
- 2x + 4 = 0
- x = -4/2
- x = -2
- The shape of the curve is a straight line.
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Answer:
Graph of Quadratic Equation/Polynomial with its Observation are:-
Explanation:
Given: Quadratic polynomial
To find: shape of curve when cofficient of is +ve, -ve or 0.
Solution:
Consider quadratic equations
Case 1: Curve when the coefficient of is positive
⇒ x² + 2x + 4 = 0
∴ x = -1 + √3 i , -1 - √3 i
Hence, Curve is upward opening parabolic.
Again,
Case 2: Curve when the coefficient of is negative
⇒ x² + 2x + 4 = 0
∴ x = 1 - √5 , 1 + √5
Hence, Curve is downward opening parabolic.
Case 3: Curve when the coefficient of is zero
⇒ 0² + 2x + 4 = 0
⇒ 2x + 4 = 0
∴ x = -4/2 or -2
Hence, Curve is a straight line.
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