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 + .... ] + 3
= (-1/3)[x^2 - 6x + 9 - 9 ] + 3
= (-1/3)[(x-3)^2 - 9] + 3
= (-1/3(x-3)^2 + 3 + 3
= (-1/3(x-3)^2 + 6