Question

Which of the following is/are true about the nature of the curve obtained for the polynomial $y=a{x}^2+bx+c$ when a=1, b=-2, c=-3.

• A. Curve is open upward
• B. Curve is open downward
• C. Curve lies above and on the line $y=-4$
• D. Curve is symmetrical about $x=1$

Answer 1

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

The correct options are
A Curve is open upward
C Curve lies above and on the line $y=-4$
D Curve is symmetrical about $x=1$

$y=a{x}^2+bx+c$
when $a=1,b=-2,c=3$ ,$y=x^2+(-2x)+3$
Here a is positive; so the curve lies above or on the line $y=\frac{4ac-b^2}{4a}$ and it is symmetric about $x=\frac{-b}{2a}$.
Thus the curve lies above and the line $y=-4$ and is symmetrical about $x=1$.