Question

The best method for solving a quadratic written in vertex form is

Answer 1

Use the square-root method. For a quadratic in vertex form y = a(x − h)^2 + k, set y = 0 and solve:

1. a(x − h)^2 + k = 0
2. a(x − h)^2 = −k
3. (x − h)^2 = −k/a
4. x − h = ±√(−k/a)
5. x = h ± √(−k/a)

If −k/a < 0 there are no real roots (you get complex roots instead). Example: 2(x − 3)^2 − 8 = 0 → (x − 3)^2 = 4 → x = 3 ± 2 → x = 1 or 5.