Using the quadratic model, find the temperature at which the least power is used. Determine the amount...

...of power that is used at this temperature.

y = 0.560X^2 + -72.492X + 2,788.742

I used the quadratic formula, but I end up with an imaginary/complex number.
My teacher said I should find the minimum and the method I used is incorrect.

Please help x/

The quadratic formula gives you roots of an equation (where it equals zero). It doesn't give you the minimum point. Since this equation is positive everywhere, it has no real roots.

You probably want to take the derivative and find the root of that equation. That will give you locations where the slope is zero (a minimum or a maximum for a quadratic equation).

EDIT: Does this class not assume calculus?

The derivative of a polynomial function is one of the first things you learn in calc I. That's too much to explain in an answer, but the mechanics are:

For each term in a function of the form Ax^n
You can create a derivative with the term: (A*n)(x^(n-1))
So 0.560x^2 becomes 2 * 0.560 x => 1.12x
-72.492X becomes 1 * (-72.492) => -72.492
and 2788.742 becomes 0 * 2788.742 => 0

Getting the zero of that function shows the location where the original function has a slope of zero.

1.12x - 72.492 = 0
1.12x = 72.492
x = 72.492/1.12 = 64.725