1.

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»

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.


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