Answer:
![f(x)=-1(x-2)^2+8](https://tex.z-dn.net/?f=f%28x%29%3D-1%28x-2%29%5E2%2B8)
Step-by-step explanation:
Given:
The quadratic function is given as:
![f(x)=-x^2+2x+4](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B2x%2B4)
The standard form of a quadratic function is given as:
, where, 'a', 'h' and 'k' are real numbers.
Now, in order to convert the given function to standard form, we use completing by square method.
![-x^2+2x=-(x^2-2x)=-[(x-2)^2-2^2]=-[(x-2)^2-4]=-(x-2)^2+4](https://tex.z-dn.net/?f=-x%5E2%2B2x%3D-%28x%5E2-2x%29%3D-%5B%28x-2%29%5E2-2%5E2%5D%3D-%5B%28x-2%29%5E2-4%5D%3D-%28x-2%29%5E2%2B4)
Now,
can be rewritten as:
![f(x)=-(x-2)^2+4+4\\f(x)=-1(x-2)^2+8](https://tex.z-dn.net/?f=f%28x%29%3D-%28x-2%29%5E2%2B4%2B4%5C%5Cf%28x%29%3D-1%28x-2%29%5E2%2B8)
Therefore, the standard form of the function is:
![f(x)=-1(x-2)^2+8](https://tex.z-dn.net/?f=f%28x%29%3D-1%28x-2%29%5E2%2B8)