Answer:
see explanation
Step-by-step explanation:
The vertex form of f(x) is
f(x) = (x - h)² + k
where (h, k) are the coordinates of the vertex
To obtain this form use the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 14x
f(x) = x² + 2(7)x + 49 - 49 + 36
= (x + 7)² - 13
The minimum value of f(x) is the y- coordinate of the vertex
vertex = (- 7, - 13), that is minimum value = - 13
