Question

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Answer 1

Answer:

f(x) = (x-4)² + 1Step-by-step explanation:

For clarity, exponents should be marked with a ^:  f(x) = x^2 - 8x + 17

Group like terms

f(x) = (x² - 8x) + 17

Complete the square

 coefficient of x term: -8

 divide coefficient in half: -4

 square the result: (-4)² = 4²

 use 4² to complete the square and keep the equation balanced:

f(x) = (x² - 8x + 4²) - 4² + 17

f(x) = (x-4)² + 1