Final answer:
To complete the square for the expression y^2 + 14y + __ and make it a perfect square trinomial, one must add the square of half the linear coefficient, which in this case is 49, making the correct answer A) 49.
Step-by-step explanation:
To make the expression y² + 14y + __ a perfect square, we need to complete the square by finding a number that, when added to the expression, creates a perfect square trinomial. This number is the square of half the coefficient of y in the linear term. Since the coefficient of y is 14, half of this coefficient is 7. Squaring 7 gives us 49, which is the number we need to add to the expression to complete the square. So, the expression becomes y² + 14y + 49, which is now a perfect square trinomial (y + 7)².