Olá!

As coordenadas do vértice são dadas por :

Xv = -b/2a

Yv = -Δ/4a

a) f(x) = x²-2x+3

Xv = -b/2a = -(-2)/2.1 = 1 <- COORD.

Para achar a outra coordenada precisamos calcular o Δ :

Δ = b²-4ac = 4-4.1.3 = -8

Yv = -Δ/4a = -(-8)/4.1 = 2 <- COORD.

b) f(x) = 4x²+4

Xv = -b/2a = 0/2.4 = 0 <- COORD.

Δ = b²-4ac = -4.4.4 = -64

Yv = -Δ/4a = -(-64)/4.4 = 64/16 = 4 <- COORD.

c) f(x) = 3x²-2x+1

Xv = -b/2a = -(-2)/2.3 = 2/6 = 1/3 <- COORD.

Δ = b²-4ac =4-4.3.1 = -8

Yv = -Δ/4a = -(-8)/4.3 = 8/12 = 2/3 <- COORD.

Espero ter ajudado! :)