Y=x^2 is shifted down by 3 units and 2 units to the left what is the new parabla

Answer 1

Horizontal movement "goes with" the x, but opposite.

y = (x + 2)²

Vertical movement goes outside the x.

y = (x + 2)² - 3

So, moving the parabola right 5 and up 6 would be...

y = (x - 5)² + 6

Answer 2

Shift 2 units to the left: f(x) → f(x + 2)

Shift down 3 units: f(x) → f(x) - 3

Put these together.

x² → (x + 2)² - 3