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!

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.