What is the equation of a parabola that has moved 5 units to the left and 3 units down?

Answer 1

A parabola has the equation y = x².

Moving horizontally goes "with" the x but with the opposite sign.

y = (x + 5)²

Vertical movement goes "outside."

y = (x + 5)² - 3

Answer 2

If the equation of the original parabola is

y = f(x),

the equation of the parabola shifted 5 units to the left an 3 units down is

g(x) = f(x + 5) - 3