Find all numbers a for which the graph of y=x^2+a and the graph of y=ax intersect. Express your answer in interval notation.

y = x^2 + a y =ax

Set these equal

x^2 + a = ax

x^2 -ax + a = 0

The discriminant is

a^2 - 4a

To have real solutions.....this must be ≥ to 0....so

a^2 - 4a ≥ 0

a ( a - 4) ≥ 0

This will be true for a on these intervals : (-inf, 0 ] U [ 4, inf)