Question

Write an equation for a parabola opening upward, shifted 6 units right, and three units down

Answer 1

y = (x-6)²-3

1) Let's write a transformation described as it is, algebraically speaking.

• opening upward, (a >0)

,

• shifted 6 units right, (-6)

,

• and three units down​ -3

2) Starting from the parent function y=x², then we can write:

y = (x-6)²-3

Notice that the horizontal shift is within the parentheses with a swapped sign. And outside that -3 indicating the vertical shift.