Question

PLLLLLEEEEEEASSSSSSE HEEEELP

Answer 1

Greetings from Brasil...

The vertex is coordinates are given by:

V = (-b/2a ; -Δ/4a)

P(X) = (X + 3)² + 2   (notable products)

(X + 3)² = X² + 2.X.3 + 3² = X² + 6X + 9   so

P(X) =  X² + 6X + 9 + 2

P(X) =  X² + 6X + 11

- b/2a = - 6/2.1 = - 3

-Δ/4a

Δ = b² - 4.a.c

Δ = 6² - 4.1.11

Δ = 36 - 44

Δ = - 8

- Δ/4a = - (- 8)/4.1 = 8/4 = 2

V = (-3; 2)

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translation = f(x) + c ⇒ P(X) + c

P(X) + c = (X + 3)² + 2 + c

P(X) + 3 = (X + 3)² + 2 + 3

Q(X) =  (X + 3)² + 5

The translation was only upwards, so the coordinate X does not change (only Y), so

V = (-3; 2 + 3)

V = (-3; 5)