f(x + q) - left q units
f(x - q) - right q units
f(x) + q - up q units
f(x) - q - down q units
-f(x) - symmetry with respect to the x--xaxis
f(-x) - symmetry with respect to the y-axis
y = - x² + 3 = -(x² - 3)
3 units down and next symmetry with respect to the x axis.
Look at the picture.