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