Answer:
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
