What transformation of the parent function, f(x) = x^2, is the function f(x) = -(x + 2) ^2

f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ f(x) = x²

∵ The parent function is f(x) = - (x + 2)²

- There is a negative out the bracket means we change f(x) to -f(x)

∴ f(x) is reflected across the x-axis

- The x is changed to x + 2, that means we translate the f(x) to the

  left two units

∵ x in f(x) is changed to (x + 2)

∴ f(x) is translated 2 units to the left

∴ f(x) reflects across the x-axis and translate left 2

the diver is 33 feet below the surface.

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