The key to this is the point (1,-3) That point must be found first. C is incorrect because you are using 3 not - 3 which does not change (as C has changed it) through out the problem.
A is using (-1,-3) which makes it wrong. Also the equation is y = -abs(x-1) - 3 which is also a mistake. The given graph points upwards not downwards.
D has it's min point at (-1,-3) which is not correct.
You are left with b which opens upwards (correct) has it's min at (1,-3) [also correct] so the answer is
