What is the equation of the translated function?

a. f(x) = (x – 1)2 – 5
b. f(x) = (x + 1)2 + 5
c. f(x) = (x – 5)2 – 1
d. f(x) = (x + 5)2 + 1

B

Step-by-step explanation:

The vertex of the original function is (0, 0 )

The vertex of the translated function is (- 1, 5 )

Given f(x) then f(x + a) represents a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

The translated graph has been shifted 1 unit left, thus

f(x) = (x + 1)²

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

The translated graph has been shifted 5 units up, thus

f(x) = (x + 1)² + 5 ← equation of translated function

step-by-step explanation:

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