Answer:
f(x) = (x - 3)² - 6
Step-by-step explanation:
To complete the square, we need to subtract 3 from both sides first
f(x) = x² - 6x + 3
- 3 - 3
f(x) - 3 = x² - 6x
Then add 9 to both sides since it is the square of half of b (6)
f(x) - 3 + 9 = x² - 6x + 9
f(x) + 6 = x² - 6x + 9
Factor the polynomial, x² - 6x + 9
f(x) + 6 = x² - 6x + 9
f(x) + 6 = (x - 3)(x - 3)
f(x) + 6 = (x - 3)²
Finally, subtract 6 from both sides
f(x) + 6 = (x - 3)²
- 6 - 6
f(x) = (x - 3)² - 6
With this vertex form equation, we know the vertex is (3, -6)
