Given f(x) = x^2 + 14x + 40 . enter the quadratic function in vertex form in the box. f(x)=

Recall that the vertex form of a quadratic function (or parabolic function) is equal to



Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.

One concept that we must remember when completing the square is that

(a + b)² = a² + 2ab + b²

So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.

So, going back to the function, we have






Thus, we have derived the vertex form of the function. 

f(x) = (x + 7)² - 9

Ithink the answer is: it is likely.