Question

What number completes the square for the function f(x) = x^2 + 8x + ___?

A) 64
B) 16
C) 4
D) 32

Answer 1

The number that completes the square for the quadratic function f(x) = x^2 + 8x + ___ is 16, resulting in the perfect square trinomial (x + 4)^2.

The correct option is C.

Step-by-step explanation:

To complete the square for the quadratic function f(x) = x^2 + 8x + ___, you need to find a number that, when added to x^2 + 8x, will make it a perfect square trinomial.

To do this, you take the coefficient of the x term, divide it by 2, and then square the result. In this case, the coefficient is 8. Dividing by 2 gives us 4, and squaring 4 gives us 16.

Therefore, the number that completes the square is 16, which makes the equation f(x) = (x + 4)^2.

The correct option is C.