Question

Determine the vertex of the function f(x) = 2(x − 5)2 + 8.

(8, −5)
(8, 5)
(−5, 8)
(5, 8)

Answer 1

Answer:

Vertex ( 5 ,8) .

Step-by-step explanation:

Given  : f(x) = 2(x − 5)² + 8.

To find : Determine the vertex of the function .

Solution : We have given

f(x) = 2(x − 5)² + 8.

Vertex form of parabola  : f (x) = a(x - h)² + k, where (h, k) is the vertex.

On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.

a = 2 , h = 5 , k = 8 .

Vertex ( 5 ,8) .

Therefore, Vertex ( 5 ,8) .

Answer 2

Answer: (5,8)

Step-by-step explanation:

The given function :$f(x) = 2(x - 5)^2 + 8.$

We know that the vertex form of a quadratic equation is given by :

$f (x) = m(x - a)^2+ b$   (1)

, where (a,b)= Vertex of the function f(x).

When we compare the given function $f(x) = 2(x - 5)^2 + 8.$ to equation (1) , we conclude that the given function is already in its vertex form.

with a= 5 and b= 8

Therefore , the vertex of the function $f(x) = 2(x - 5)^2 + 8.$ = (5,8)