Answer:
g(x) = x² - 7x + 16
Explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
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f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):
g(x) = (x - 3)² - (x - 3) + 4 use (a - b)² = a² - 2ab + b²
g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4
g(x) = x² - 6x + 9 - x + 3 + 4 combine like terms
g(x) = x² + (-6x - x) + (9 + 3 + 4)
g(x) = x² - 7x + 16