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

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

ANSWER

The vertex form is

EXPLANATION

The given function is

This is the same as:

We add and subtract the square of half the coefficient of x.

The first three term is a perfect square trinomial:

The vertex form is

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

5

step-by-step explanation: