Question

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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Answer 1

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.

Answer 2

Answer:

Graph of Quadratic Equation/Polynomial with its Observation are:-

Explanation:

Given: Quadratic polynomial

To find: shape of curve when cofficient of $x^{2}$ is +ve, -ve or 0.

Solution:

Consider quadratic equations $x^{2} + 2x + 4 = 0 , -x^{2} + 2x +4 = 0$

Case 1:  Curve when the coefficient of $x^{2}$ 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 $x^{2}$ is negative

⇒ x² + 2x + 4 = 0

∴ x = 1 - √5 , 1 + √5

Hence, Curve is downward opening parabolic.

Case 3: Curve when the coefficient of $x^{2}$ is zero

⇒ 0² + 2x + 4 = 0

⇒ 2x + 4 = 0

∴ x = -4/2 or -2

Hence, Curve is a straight line.

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