Answer:
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
