Find the vertex of f(x) = 2x^2 +6x +10
a.) (3 , 0)
b.) (-1.5,4,5)
c.) (-3,4)
d.) (-1.5, 5.5)

Step-by-step 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!