Question

What is the vertex form of `y=(3x - 15)(x - 5)`?

Answer 1

`y=3(x-5)^2+0`

Explanation:

The vertex form of a quadratic equation is

`y = a(x-h)^2+k`

and `(h,k)` is the vertex of the parabola the equation represents.

Normally, to find the vertex form, we use a process called completing the square. In this case, however, we can simply factor our `3` from the first factor and we are essentially done.

`(3x-15)(x-5) = 3(x-5)(x-5)`

`=3(x-5)^2+0`

Thus the vertex form is `y = 3(x-5)^2+0`