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!

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.