Question

Directions: Identify the roots of the quadratic function.

f(x)= -(x-2)^2+4​​

Answer 1

The roots of the quadratic function f(x) = -(x-2)^2+4 are x = 0 and x = 4.

Step-by-step explanation:

The roots of the quadratic function f(x) = -(x-2)^2+4 can be determined by setting the equation equal to zero and solving for x. Here are the steps:

1. Start with the equation f(x) = -(x-2)^2+4
2. Set f(x) equal to zero: -(x-2)^2+4 = 0
3. Expand and simplify the equation: -x^2+4x-4+4 = 0
4. Combine like terms: -x^2+4x = 0
5. Factor out x: x(-x+4) = 0
6. Set each factor equal to zero and solve for x: x = 0 or x - 4 = 0
7. The roots of the quadratic function f(x) = -(x-2)^2+4 are x = 0 and x = 4