Hello from MrBillDoesMath!
Answer: Choice C
Discussion:
The y-intercepts are the x values where y = 0. Substituting y = 0 in the equation gives
(x+2)^2 + (0-4)^2 = 13 =>
(x+2)^2 + 16 = 13 =>
Subtract 16 from both sides
(x+2)^2 = 13 - 16 = -3 (*)
The square of a real number is greater than or equal to 0. (Not true for complex numbers). The left side of (*) is therefore >= 0 but as also equals -3. This is not possible so there is no solution to the equation. Choice C.
Thank you,
MrB
