Answer:
f(x) = 2(x + 1)² + 1
Explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms
= 2(x² + 2x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 2x
f(x) = 2(x² + 2(1)x + 1 - 1) + 3
= 2(x + 1)² - 2(1) + 3
= 2(x + 1)² - 2 + 3
= 2(x + 1)² + 1 ← in vertex form