A quadratic relation has zeros 2 and 6, and it has an optimal value of 3. Determine the equation of the relation in factored form.

y = (-3/4) * (x - 2) * (x-6)

Step-by-step explanation:

Ok, we can write a quadratic equation as:

Y = a * (x - b) * (x - c)

where a is a scalar, b and c are the roots.

We know that b = 2 and c = 6, so we have:

y = a * (x - 2) * (x - 6)

now, we can expand this and get:

y = a * (x^2 - 8x + 12)

The optimal value of this quadratic equatin is when:

x = 8/2 = 4

So we have that when x = 4, we must have y = 3.

3 = a * (4^2 - 8*4 + 12) = a*-4

a = - 3/4.

Our quadratic equation is:

y = (-3/4) * (x - 2) * (x-6)