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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.

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

2 Answers

6 votes

Answer:

A. Maximum at (1, 1)

Explanation:

User Arok
by
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3 votes

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)

User Cameron Forward
by
8.4k points

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