Express the function f(x) = −[ 1/3]x^2 + 2x + 3 in the form f(x) = a(x + p)^2 + q by completing the square:

Question

f(x) = −[ 1/3]x^2 + 2x + 3

Answer 1

f(x) = −[1/3]x^2 + 2x + 3
= -(1/3)(x^2 -6x -9)
= -(1/3)(x^2 -6x +9 -18)
= -(1/3)(x-3)^2 + 6