Question

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

Answer 1

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.