What is the vertex of the absolute value function defined by f (x) = |x-2| - 7

The vertex of the function f (x) is at (2,-7)

Step-by-step explanation:

The function is given to be f (x) = |x-2| - 7

Now, f (x) = x - 2 - 7 = x - 9 for, (x - 2) ≥ 0, ⇒ x ≥ 2 ... (1)

and f (x) = 2 - x - 7 = - x - 5 for, (x - 2) < 0, ⇒ x < 2 ... (2)

Now, solving equation (1) and (2), we get, x - 9 = - x - 5

⇒ 2x = 4

⇒ x = 2

And hence, from equation (1) we get, y = x - 9 = 2 - 9 = - 7

Therefore, the vertex of the function f (x) is at (2,-7) (Answer)