Question

which must be true of a quadratic function whose vertex is the same as its y-intercept? the axis of symmetry for the function is x = 0. the axis of symmetry for the function is y = 0. the function has no x-intercepts. the function has 1 x-intercept.

Answer 1

a. The axis of symmetry for the function is x = 0.

Explanation:

edge 2020

Answer 2

If quadratic function
`y=ax^2+bx+c` has vertex that is the same as its y-intercept, then

`x_v=-(b)/(2a)=0,\\ \\b=0`

and its equation is
`y=ax^2+c.`

The graph of this quadratic function is translated graph of the function
`y=ax^2` 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
`y=ax^2` is x=0 (y-axis).

Answer: correct choice is A