Question

The above picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

Based on the above information, answer the following questions.

If the parabolic arch is represented by a polynomial $a{x}^2+bx+c$, which of the following is mandatory?

• A. $a\ne 0$
• B. $b\ne 0$
• C. $c\ne 0$
• D. $a=0,c\ne 0$

Answer 1

The correct option is A $a\ne 0$

Since the parabolic arch is represented by $a{x}^2+bx+c$, the coefficient of $x^2$ should not be 0.

Suppose if $a=0,$ the polynomial becomes $bx+c$ which is linear.

Hence, the coefficent of $x^2$, ie $a$ can never be 0.