Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8 + x^2 + 7 ?

The function translated 4 units right and 9 units down

The third answer

Step-by-step explanation:

* To solve the problem you must know how to find the vertex

  of the quadratic function

- In the quadratic function f(x) = ax² + bx + c, the vertex will

 be (h , k)

- h = -b/2a and k = f(-b/2a)

* in our problem

∵ f(x) = x²

∴ a = 1 , b = 0 , c = 0

∵ h = -b/2a

∴ h = 0/2(1) = 0

∵ k = f(h)

∴ k = f(0) = (0)² = 0

* The vertex of f(x) is (0 , 0)

∵ g(x) = -8x + x² + 7 ⇒ arrange the terms

∴ g(x) = x² - 8x + 7

∵ a = 1 , b = -8 , c = 7

∴ h = -(-8)/2(1) = 8/2 = 4

∵ k = g(h)

∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9

∴ The vertex of g(x) = (4 , -9)

* the x-coordinate moves from 0 to 4

∴ The function translated 4 units to the right

* The y-coordinate moves from 0 to -9

∴ The function translated 9 units down

* The function translated 4 units right and 9 units down

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