Question

Ariel completes the square for the function (y = x² - 16x+ 17). Which of the following functions reveals the vertex of the parabola?

a) (y = (x - 8)² + 1)
b) (y = (x + 8)² - 1)
c) (y = (x - 8)² - 1)
d) (y = (x + 8)² + 1)

Answer 1

Completing the square for the function (y = x² - 16x + 17) involves finding the proper constant to add and subtract to transform it into vertex form. The closest answer given is (a) (y = (x - 8)² + 1), but none match the exact form calculated, which should be (y = (x - 8)² - 30).

Step-by-step explanation:

To complete the square for the function (y = x² - 16x + 17) to reveal the vertex of the parabola. To complete the square, we can follow these steps:

1. Rewrite the quadratic term and the linear term, leaving space to add a new constant: y = x² - 16x + __ + 17.
2. Find the number to complete the square by taking half of the linear coefficient and squaring it: (-16/2)² = 64.
3. Add and subtract this number inside the bracket and then simplify: y = (x² - 16x + 64) - 64 + 17.
4. Rewrite the equation in the proper form: (y = (x - 8)² - 47 + 17).
5. Finally, add 47 to 17 to get the complete squared equation: (y = (x - 8)² - 30).

Therefore, the correct answer is none of the functions listed since they do not have the correct constant term. However, the expression closest to the completed square form is (y = (x - 8)² + 1), meaning the correct answer would be closest to answer choice (a), but adjusted for the constant term.