Question

Using the completing-the-square method, find the vertex of the function f(x) = –3x^2+ 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

I just took the test and the answer is NOT b

Explanation:

Answer 2

f(x) = -3x² + 6x - 2
y = -3x² + 6x - 2
y + 2 = -3x² + 6x
y + 2 = -3(x²) - 3(2x)
y + 2 = -3(x² + 2x)
y + 2 - 3(1) = -3(x² + 2x + 1)
y + 2 - 3 = -3(x² + x + x + 1)
y - 1 = -3(x(x) + x(1) + 1(x) + 1(1))
y - 1 = -3(x(x + 1) + 1(x + 1))
y - 1 = -3(x + 1)(x + 1)
y - 1 = -3(x + 1)²
y = -3(x + 1)² + 1
f(x) = -3(x + 1)² + 1
f(x) = -3(x - (-1))² - (-1)

The answer is B.