You need to complete the square. Notice that

(x-5)^2 = x^2 – 10x + 25.

Therefore

f(x) = x^2 -10x + 33

= (x^2 -10x + 25) – 25 + 33

= (x – 5)^2 + 8

You have:

a=1,

h=5,

k=8

f(x) = x^2 – 10x + 33 = x^2 -10x + 25 + 8 = (x-5)^2 + 8

(a = 1; h = 5; k = 8)

f(x)= x^2 – 10x + 33

f(x)= (x^2-10x+25)+33-25

= (x-5)^2 + 8

gudluck

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