Question

I need help on this problem ​

Answer 1

y² - 2y - 4x + 9 = 0 (*)

a = 1 b = -2 c = -4x + 9

Δ = b² - 4ac = 4 - 4(9 - 4x) = 4 - 36 + 16x = 16x - 32

if (*) have the solutions => Δ ≥ 0

⇔ 16x - 32 ≥ 0 ⇔ x ≥ 2

with x ≥ 2 => y =
`(2+√(16x-32) )/(2)=(2+4√(x-2) )/(2)=1+2√(x-2)`

or y =
`1-2√(x-2)`

Explanation: