Question

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

Answer 1

Vertex form of the function will be f(x) = (x - 1)² + 3.

Explanation:

Vertex form of a quadratic function is given by f(x) = a(x - h)² + k

where (h, k) is the vertex of the given parabola.

Now we will convert the function in the vertex form.

f(x) = x² - 2x + 1 + 3

= (x - 1)² + 3

Therefore, the vertex form of the function will be f(x) = (x - 1)² + 3

and the vertex will be (1, 3).

Answer 2

The question is asking us to find which function in the vertex form is equivalent to f ( x ) = 4 + x^2 - 2 x. We have to add 1 to make a squared binomial ( and also to subtract 1 ). f ( x ) = ( x^2 - 2 x + 1 ) - 1 + 4 = ( x - 1 )^2 + 3. Then we have the vertex point ( 1, 3 ). Answer: The function in vertex form is: f ( x ) = ( x - 1 ) ^2 + 3.