a)
f(x) = (x - 1)² + 3
f(x) = x² - 2x + 1 + 3
f(x) = x² - 2x + 4
b)
f(x) = -2(x - 5)(x + 2)
f(x) = -2(x² + 2x - 5x - 10)
f(x) = -2(x² - 3x - 10)
f(x) = -2x² + 6x + 20
c)
f(x) = -1/2(x + 2/3)² - 7/9
f(x) = -1/2(x² + 4/3x + 4/9) - 7/9
f(x) = -1/2x² - 2/3x - 2/9 - 7/9
f(x) = -1/2x² - 2/3x - 1