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nignag [31]
3 years ago
15

Write the quadratic function in standard form. f(x) = -x2 + 2x + 4 f(x) =

Mathematics
1 answer:
goldenfox [79]3 years ago
7 0

Answer:

f(x)=-1(x-2)^2+8

Step-by-step explanation:

Given:

The quadratic function is given as:

f(x)=-x^2+2x+4

The standard form of a quadratic function is given as:

f(x)=a(x-h)^2+k, 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

Now, f(x)=-x^2+2x+4 can be rewritten as:

f(x)=-(x-2)^2+4+4\\f(x)=-1(x-2)^2+8

Therefore, the standard form of the function is:

f(x)=-1(x-2)^2+8

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