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)

we have

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

Let

y=f(x)

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

Factor the leading coefficient

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

Rewrite as perfect squares

the vertex is the point

therefore

the answer is the option

A. Maximum at (1, 1)

linear pair postulates

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step-by-step explanation: