Question

To draw a graph of a quadratic polynomial and observe:- in) The shape of graph when the coefficient of x^(2) is positive ii) The shape of graph when the coefficient of x^(2) is negative iii) Its zero.​

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 a 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.