Answer:
y = √(4x - 8) - 3
Explanation:
y = 1/4(x + 3)² + 2
To find the inverse, switch the places of the x and y.
x = 1/4(y + 3)² + 2
Solve for y.
x - 2 = (1/4(y + 3)² + 2) - 2
x - 2 = 1/4(y + 3)²
4(x - 2) = 4(1/4(y + 3)²)
4x - 8 = (y + 3)²
√(4x - 8) = √((y + 3)²)
√(4x - 8) = y + 3
√(4x - 8) - 3 = (y + 3) - 3
√(4x - 8) - 3 = y
y = √(4x - 8) - 3