y=1/2(x+1)(x-3)

Question

Can you change this to vertex form and show your steps

Answer 1

There are several ways to do this problem, including "completing the square". I'll pick what I would call the easiest way:

The vertex form is y = a(x - k)² + k where (h, k) is the vertex. The "a" value in this case is 1/2. So the easiest way to write this in vertex form is to find the vertex (the easiest way) and then plug it into the equation.

The x-value of the vertex is halfway between the two x-intercepts. The x-intercepts are -1 and 3. (-1 + 3)/2 = 1.

So the x-coordinate of the vertex (h) is 1.

To find the y-coordinate of the vertex, plug in x = 1:

y = 1/2(1 + 1)(1 - 3) = 1/2(2)(-2) = -2 (or k = -2)

So the vertex form is y = 1/2(x - 1)² - 2