Let fx 3x2 6x 1 and gx 3x2 5 a Complete the square in x

Let f(x) = 3x^2 + 6x - 1 and g(x) = 3x^2 + 5 (a) Complete the square in x to write f(x) in the form f(x) = a(x - h)^2 + k.

Solution

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Given

f(x) = 3x^2 + 6x - 1

f(x) = 3 (x^2 + 2x ) - 1

Completing squares

f(x) = 3 (x^2 + 2x + 1 - 1) - 1

f(x) = 3 (x^2 + 2x + 1) - 4

f(x) = 3 (x + 1)^2 - 4

Solution