Graph the function.
g(x) = -1/5(x+5)^2-2

Step-by-step explanation:

The first one is Crosses the axis at (1, 0). The second one is Crosses the axis at (−4, 0). The third one is touching the axis at (−5, 0).

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

Step-by-step explanation:

Let us revise the translation

1. If the function f(x) translated horizontally to the right by h units, then

   its image is g(x) = f(x - h)

2. If the function f(x) translated horizontally to the left by h units, then

   its image is g(x) = f(x + h)

3. If the function f(x) translated vertically up by k units, then its image

   is g(x) = f(x) + k

4. If the function f(x) translated vertically down by k units, then its image

   is g(x) = f(x) - k

∵ f(x) = x²

∵ g(x) = (x - 5)² - 9

∴ g(x) = f(x - 5)² - 9

∴ h = 5 ⇒ 5 units right

∴ k = -9 ⇒ 9 units down

∴ f(x) translated 5 units to the right

∴ f(x) translated 9 units down

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down