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Using the completing-the-square method, rewrite f(x) = x² - 8x + 3 in vertex form.

1) f(x) = (x - 8)²
2) f(x) = (x - 4)² - 13
3) f(x) = (x - 4)² + 3
4) f(x) = (x - 4)² + 16

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Final answer:

To rewrite the function f(x) = x² - 8x + 3 in vertex form using the completing-the-square method, you end up with f(x) = (x - 4)² - 13, corresponding to option 2.

Step-by-step explanation:

To rewrite the quadratic function f(x) = x² - 8x + 3 in vertex form using the completing-the-square method, we will follow these steps:

  1. Consider the quadratic and linear terms: x² - 8x.

  2. Divide the coefficient of x by 2 and square it: (-8 / 2)² = 16.

  3. Add and subtract this number inside the function to complete the square: f(x) = (x² - 8x + 16) - 16 + 3.

  4. Rewrite the trinomial as a perfect square and simplify the constants: f(x) = (x - 4)² - 13.

Therefore, the quadratic function in vertex form is f(x) = (x - 4)² - 13, which matches option 2.

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