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.

Maximum at (1, 1)
Minimum at (1, 1)
Maximum at (−1, 2)
Minimum at (−1, 2)

Answer 1

Max (1,1)

Explanation:

The parabola is opening down, so this would be the highest point.

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

The x for the vertex is found

`(-b)/(2a)` b is 6 and a is -3

`(-6)/(2(-3))` =
`(-6)/(-6)` = 1

The x value of the vertex is 1.

To find the y value, plug 1 in for x and solve for y

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

-3(
`1^(2)`) + 6(1) -2

-3 + 6 - 2

3 - 2

1

The y value of the vertex is 1.

The ordered pair for the vertex would be (1,1).

Helping in the name of Jesus.