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)