Question

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

Answer 1

The vertex form is

`f(x) = {(x - 1)}^(2) + 3`

EXPLANATION

The given function is

`f(x) = 4 + {x}^(2) - 2x`

This is the same as:

`f(x) = {x}^(2) - 2x + 4`

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

`f(x) = {x}^(2) - 2x + {( -1 )}^(2) - {( -1 )}^(2) + 4`

`f(x) = {x}^(2) - 2x + 1 - 1 + 4`

The first three term is a perfect square trinomial:

`f(x) = {(x - 1)}^(2) + 3`

The vertex form is

`f(x) = {(x - 1)}^(2) + 3`

Answer 2

option A

f(x) = (x – 1)2 + 3

Explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

Step 1

f(x) = 4 + x² – 2x

here a = 1

b = -2

c = 4

Step 2

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