Explanation:
To find the vertex of 2x^2 + 6x + 10, you must complete the square.
(2x^2 + 6x ) + 10 <------- start by separating constant from variable terms
2 (x^2 + 3x ) + 10 <------ factor out the coefficient of first term
2 (x^2 + 3x + 2.25) + 10 - 4.5 <--- divide coefficient of x-term by 2, square result. then add inside parenthesis and subtract outside parenthesis (after multiplying it by 2 because we factored it out)
2 (x^2 + 3x + 2.25) + 10 - 4.5 <--- then simply factor trinomial and simplify outside constant terms
after factoring and simplifying, you should have 2 (x + 1.5)^2 + 5.5, which is vertex form.
you can find the vertex from vertex form, so the vertex is (-1.5, 5.5), or option D.
have a good day!