Sorry but i need your (again) :

given the quadratic function f(x)= 3x²- 6x + 1

express the quadratic function f(x) in the form a(x+p)²+q, where a, p and q are constants. determine whether f(x) has a maximum or minimum value and state the value.

see explanation

Step-by-step explanation:

Given

f(x) = 3x² - 6x + 1

To express in vertex form

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Use the method of completing the square

The coefficient of the x² must be 1, so factor out 3

f(x) = 3(x² - 2x) + 1

add/subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = 3(x² + 2(- 1)x + 1 - 1) + 1

     = 3(x - 1)² - 3 + 1

     = 3(x - 1)² - 2 ← in vertex form

with vertex = (1, - 2)

To determine if vertex is a max/ min

• If a > 0 then minimum

• If a < 0 then maximum

here a = 3 > 0 ⇒ minimum at (1, - 2)

The minimum value is the y- coordinate of the vertex, that is

minimum value = - 2