What is the sum of all numbers a for which the graph of y=x^2+a and the graph of y=2ax intersect one time?
Set the y's equal
x^2 + a = 2ax
x^2 - 2ax + a = 0
If these intersect once then......
(2a)^2 - 4a = 0
4a^2 - 4a = 0
a^2 - a = 0
a ( a - 1) = 0
Set each factor to 0 and solve for a and we get that
a = 0 and a = 1
The sum is 1
