Thank you for the opportunity to help you with your question!

(a)

f(x) = 2x^{2} + 4x + 3

= (2x^{2}
+ 4x + 2) + 1

= 2(x^{2} +
2x + 1) + 1

= 2(x + 1)^{2} + 1

(b)

Vertex: (x, y) = (-1, 1)

x-intercept: none

y-intercept: (0, 3)

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