Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point.

minimum at (2, - 2 )

Step-by-step 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

If a > 0 then the vertex is a minimum

If a < 0 then the vertex is a maximum

Given

f(x) = 2x² - 8x + 6 ← factor out 2 from the first 2 terms

     = 2(x² - 4x) + 6

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 4x

f(x) = 2(x² + 2(- 2)x + 4 - 4) + 6

     = 2(x - 2)² - 8 + 6

     = 2(x - 2)² - 2 ← in vertex form

with vertex = (2, - 2) and a > 0

Thus minimum at (2, - 2 )

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours