Question

Choose the correct statements regarding the nature of curve formed by the graphical representation of the polynomial $a{x}^2+bx+c$ when $a=2,b=0,c=0$.

• A. Curve is open upwards
• B. Curve lies above and on the line $y=0$
• C. Curve is symmetric about $x=0$
• D. Curve is symmetric about y axis

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Curve is open upwards
B Curve lies above and on the line $y=0$
C Curve is symmetric about $x=0$
D Curve is symmetric about y axis

Given $a=2,b=0$ and $c=0$, the polynomial becomes $y=2x^2$.
If $a>0$, the curve is open upward.
The curve lies above or on the line $y=\frac{4ac-b^2}{4a}$ and it is symmetric about $x=\frac{-b}{2a}$.
By solving, the curve lies on the line $y=0$ and is symmetric about $x=0\Rightarrow$ curve is symmetric about the y-axis.