Question

Using the completing-the-square method, find the vertex of the function f(x) = –3x2 + 6x − 2 and indicate whether it is a minimum or a maximum and at what point.

A. Maximum at (1, 1)
B. Minimum at (1, 1)
C. Maximum at (–1, 2)
D. Minimum at (–1, 2)

Answer 1

A. Maximum at (1, 1)

Explanation:

Answer 2

we have

`f(x) =-3x^(2)+ 6x-2`

Since the leading coefficient is negative, the function has a maximum

Let

y=f(x)

`y=-3x^(2)+ 6x-2`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y+2=-3x^(2)+ 6x`

Factor the leading coefficient

`y+2=-3(x^(2)-2x)`

Complete the square. Remember to balance the equation by adding the same constants to each side

`y+2-3=-3(x^(2)-2x+1)`

`y-1=-3(x^(2)-2x+1)`

Rewrite as perfect squares

`y-1=-3(x-1)^(2)`

`y=-3(x-1)^(2)+1`

the vertex is the point
`(1,1)`

therefore

the answer is the option

A. Maximum at (1, 1)