Final answer:
To identify the roots of the quadratic function f(x) = -(x - 2)^2 + 4, we set the function equal to zero, expand and rearrange, take the square root of both sides, and solve for x. The roots of the quadratic function are x = 0 and x = 4.
Step-by-step explanation:
The quadratic function is given as f(x) = -(x - 2)^2 + 4. To identify the roots, we set the function equal to zero and solve for x:
-(x - 2)^2 + 4 = 0
Expanding and rearranging, we get:
(x - 2)^2 = 4
Taking the square root of both sides, we have:
x - 2 = ±2
Solving for x, we get two possible values for the roots:
x = 2 ± 2
Therefore, the roots of the quadratic function are:
x = 0 and x = 4