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

(a) f(x) = (x – 1)2 + 3
(b )f(x) = (x – 1)2 + 5
(c) f(x) = (x + 1)2 + 3
(d) f(x) = (x + 1)2 + 5

option A

f(x) = (x – 1)2 + 3

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