what is the vertex of the absolute value function defined by f(x) = |x-2| -7 Question what is the vertex of the absolute value function defined by f(x) = |x-2| -7 in progress 0 Math Josie 2 weeks 2021-09-10T13:12:08+00:00 2021-09-10T13:12:08+00:00 1 Answer 0

## Answers ( )

Answer: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 = 2And 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)