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Verified answer
Y = -x² + 2x + 3y = x² - 4x + 3
x² - 4x + 3= - x² + 2x + 3
2x² - 6x = 0
2x(x- 3) = 0
2x=0 ∨ x- 3= 0
x= 0 ∨ x= 3
y = x² - 4x + 3
x =0 → y = 3
x= 3 → y = 0
HP (x,y)= (0,3) ,( 3,0)