The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex of the parabola [tex]y=ax^2+bx+c[/tex] can be found as
[tex]x_v=-\dfrac{b}{2a}.[/tex]
The equation x=0 represents the y-axis, therefore, parabola should be symmetric about the y-axis. This means that parabola vertex is placed on the y-axis. If parabola vertex is placed on the y-axis, then [tex]x_v=0[/tex] and
[tex]-\dfrac{b}{2a}=0\Rightarrow b=0.[/tex]
Only third parabola has b=0, then
correct choice is C.
