I started attending class again. I found myself having to recall stuff that had long lied dormant. So I was studying and I completely fell ass backwards into a way of representing a trinomial that circumvents the need for the quadratic equation!

let's say we have X^2-6X+13

first we complete the square on the first two terms

y=x^2-3x+9

now we represent the final term as an equation equaling 13 (9+4=13)

so we get y=(x-3)^2+4

As you can see the equation is now in the form y=af(b(x-h))+k, so you can just plug in values for y or x to find corresponding values.