Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x? f(x) = (x – 1)2 + 3 f(x) = (x – 1)2 + 5 f(x) = (x + 1)2 + 3 f(x) = (x + 1)2 + 5

vertex form is f(x) = ( x-1)² + 3.

Step-by-step explanation:

Given :  f(x) = 4 + x² – 2x.

To find : Which function in vertex form is equivalent to f(x) = 4 + x² – 2x.

Solution : We have given that  f(x) = 4 + x² – 2x.

Rearrange in function :  f(x) = x² – 2x + 4.

Vertex form of y = a(x-h)²+k .

Now, add and subtract (-1)² in f(x) .

f(x) = x² – 2x + 4 + (-1)²- (-1)².

By  Squaring formula : (x +a)²= x²+ a²+2ax .

We can write x² – 2x + (-1)²- (-1)² +4 as ( x-1)²- (-1)² +4.

f(x) = ( x-1)²- (-1)² +4.

Now , completing square ,

f(x) = ( x-1)²- 1 +4.

f(x) = ( x-1)² + 3.

Therefore , vertex form is f(x) = ( x-1)² + 3.

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answer: d.) the total number of protons and neutrons is 15

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