Answer:
[tex]f(x)=-1(x-2)^2+8[/tex]
Step-by-step explanation:
Given:
The quadratic function is given as:
[tex]f(x)=-x^2+2x+4[/tex]
The standard form of a quadratic function is given as:
[tex]f(x)=a(x-h)^2+k[/tex], 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.
[tex]-x^2+2x=-(x^2-2x)=-[(x-2)^2-2^2]=-[(x-2)^2-4]=-(x-2)^2+4[/tex]
Now, [tex]f(x)=-x^2+2x+4[/tex] can be rewritten as:
[tex]f(x)=-(x-2)^2+4+4\\f(x)=-1(x-2)^2+8[/tex]
Therefore, the standard form of the function is:
[tex]f(x)=-1(x-2)^2+8[/tex]
