Answer:
(2, - 1 ) and (5, 2 )
Step-by-step explanation:
y + 2 = (x - 3)² → (1)
y + 3 = x ( subtract 3 from both sides )
y = x - 3 → (2)
Substitute y = x - 3 into (1)
x - 3 + 2 = (x - 3)² ← expand using FOIL
x - 1 = x² - 6x + 9 ( subtract x - 1 from both sides )
0 = x² - 7x + 10 ← in standard form
0 = (x - 2)(x - 5) ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 5 = 0 ⇒ x = 5
Substitute these values into (2) for corresponding values of y
x = 2 : y = 2 - 3 = - 1 ⇒ (2, - 1 )
x = 5 : y = 5 - 3 = 2 ⇒ (5, 2 )
