2(x - 2)² = 8(y + 7)
2(x - 2)(x -2) = 8(y) + 8(7)
2[x(x - 2) - 2(x - 2)] = 8y + 56
2[x(x) - x(2) - 2(x) + 2(2)] = 8y + 56
2(x² - 2x - 2x + 4) = 8y + 56
2(x² - 4x + 4) = 8y + 56
2(x²) - 2(4x) + 2(4) = 8y + 56
2x² - 8x + 8 = 8y + 56
- 56 - 56
2x² - 8x - 48 = 8y
8 8
¹/₄x² - x - 6 = y
¹/₄y² - y - 6 = x
+ 6 + 6
¹/₄y² - y = x + 6
4(¹/₄y² - y) = 4(x + 6)
4(¹/₄y²) - 4(y) = 4(x) + 4(6)
y² - 4y = 4x + 24
y² - 4y + 4 = 4x + 24 + 4
y² - 2y - 2y + 4 = 4x + 28
y(y) - y(2) - 2(y) + 2(2) = 4x + 28
y(y - 2) - 2(y - 2) = 4x + 28
(y - 2)(y - 2) = 4x + 28
(y - 2)² = 4x + 28
√(y - 2)² = √(4x + 28)
y - 2 = √4(x) + 4(7)
y - 2 = √4(x + 7)
y - 2 = 2√(x + 7)
+ 2 + 2
y = 2 ± 2√(x + 7)
The answer is D.
