Question

On the same set of axes are drawn the graph of $y=a{x}^2+bx+c$ and the graph of the equation obtained by replacing $x$ by $-x$ in the given equation. If $b\ne 0$ and $c\ne 0$ these two graphs intersect:

• A. in two points, one on the x-axis and one on the y -axis
• B. in one point located on neither axis
• C. only at the origin
• D. in one point on the x-axis
• E. in one point on the y-axis

Answer 1

The correct option is E in one point on the y-axis

For $x\ne 0,a{x}^2+bx+c\ne ax2-bx+c$;
for $x=0$, $a{x}^2+bx+c=a{x}^2-bx+c$
$\therefore$ There is one intersection point ($0$, c);
$\therefore$ (e) is the correct choice.