Quadratic Equation How to Write in Vertex Form (Easier Method)

The video introduces the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the vertex. It then highlights that the given quadratic is in general form: y = ax^2 + bx + c, and the goal is to convert it.

An easier method for finding the x-coordinate of the vertex (h) is presented using the formula x = -b / 2a. For the given equation, a = 2 and b = -4. Plugging these values into the formula yields x = -(-4) / (2 * 2) = 4 / 4 = 1. So, h = 1.

To find the y-coordinate of the vertex (k), substitute the calculated x-coordinate (1) back into the original quadratic equation. This results in y = 2(1)^2 - 4(1) + 1 = 2 - 4 + 1 = -1. Therefore, k = -1, and the vertex is (1, -1).

With the vertex (h=1, k=-1) and the 'a' value from the original equation (a=2), the quadratic can be written in vertex form: y = 2(x - 1)^2 - 1. It's crucial to remember that the sign of 'h' in the vertex form is opposite to the x-coordinate of the vertex.