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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

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ShyzaSling

Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step 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

kudzordzifrancis

ANSWER

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

EXPLANATION

The given function is

[tex]f(x) = 4 + {x}^{2} - 2x[/tex]

This is the same as:

[tex]f(x) = {x}^{2} - 2x + 4[/tex]

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

[tex]f(x) = {x}^{2} - 2x + {( -1 )}^{2} - {( -1 )}^{2} + 4[/tex]

[tex]f(x) = {x}^{2} - 2x + 1 - 1 + 4[/tex]

The first three term is a perfect square trinomial:

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

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