Question

Which equation written below in vertex form is equivalent to the equation?

Answer 1

First, consider that a quadratic equation in vertex form is given by:

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

where a is the leading coefficient and (h,k) is the vertex of the curve.

You have the following equation:

`y=x^2-6x+12`

In this case, the leading coefficient is a = 1.

The vertex is determined as follow:

Use the following formula to find h:

`h=-(b)/(2a)=-(-6)/(2(1))=3`

where we have used b = -6.

Now, to find k use:

`f(h)=(3)^2-6(3)+12=9-18+12=3`

Then, h = 3 and k = 3.

By replacing the values of a, h and k, you obtain:

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

The previous result is the given equation in vertex form.