Question

Which of the following is not the graph of a quadratic polynomial. Justify your answer

Answer 1

For any quadratic polynomial $a{x}^2+bx+c,a\ne 0$, the graph of the corresponding equation $y=a{x}^2+bx+c$ has one of the two shapes either open upwards like $\cup$ or open downwards like $\cap$ depending on whether $a>0ora<0$.

These curves are called parabolas. So, option (d) is not a quadratic polynomial.
Also, the curve of a quadratic polynomial cuts the x-axis on at most two points but in option (d) the curve cuts the x-axis at three points. So it does not represent a quadratic polynomial.