Question

Please help!! I’ve been stuck on this for hours!!

Answer 1

g(x) =
`(1)/(2)` (x - 2)² - 1

Explanation:

note that the vertex of the function x² is at (0, 0 )

given f(x) then f(x ± a ) is a horizontal translation of f(x)

• if + a then a shift to the left of a units

• if - a then a shift to the right of a units

here the vertex has been shifted 2 units to the right so

(x - 2)²

given f(x) then f(x) ± c is a vertical translation of f(x)

• if + c then a shift up of c units

• if - c then a shift down of c units

here the vertex has been shifted down by 1 unit , then

g(x) = a (x - 2)² - 1 ( a is a multiplier )

to find a substitute any point that lies on g(x) into g(x)

using (0, 1 )

1 = a(0 - 2)² - 1 ( add 1 to both sides )

2 = a(- 2)² = 4a ( divide both sides by 4 )

`(2)/(4)` = a , that is

a =
`(1)/(2)`

g(x) =
`(1)/(2)` (x - 2)² - 1 ← is the transformed function