If quadratic function [tex]y=ax^2+bx+c[/tex] has vertex that is the same as its y-intercept, then
[tex]x_v=-\dfrac{b}{2a}=0,\\ \\b=0[/tex]
and its equation is [tex]y=ax^2+c.[/tex]
The graph of this quadratic function is translated graph of the function [tex]y=ax^2[/tex] up or down (depends on c).
This means that there could be
- two x-intercepts;
- one x-intercept;
- no x-intercepts.
The axis of symmetry of the graph of the function [tex]y=ax^2[/tex] is x=0 (y-axis).
Answer: correct choice is A
