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
