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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.

AMaximum at (1, 1)
BMinimum at (1, 1)
CMaximum at (–1, 2)
DMinimum at (–1, 2)

Verified Answer :

calculista

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)

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