Answer:
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)
