Aloha! Looking for some help with an Algebra 1 equation. See photo below. Thank you in advance.

(4, 11 ) ; (- 4, 27 )

Step-by-step explanation:

Given

f(x) = x² - 2x + 3 → (1)

f(x) = - 2x + 19 → (2)

Substitute f(x) = x² - 2x + 3 into (2)

x² - 2x + 3 = - 2x + 19 ( add 2x to both sides )

x² + 3 = 19 ( subtract 3 from both sides )

x² = 16 ( take square root of both sides )

x = ± = ± 4

Substitute these values into (2) for corresponding values of y

x = 4 : y = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )

x = - 4 : y = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )