A quadratic formula is simply a y=ax^2 + bx + c equation...
Lets say the problem asks you to factor:
\(\displaystyle y = x^2 + 5x - 6\)
The firsth term is \(\displaystyle x^2\), so the first term in the facors will be x, because \(\displaystyle x*x= x^2\).
The middle term is positive, and the last term is negative. Since the second terms in the factors must multiply together to equal the third term, and they must also add up to the second term, we know that the signs must be a + and a -.
We now have for the factors:
\(\displaystyle (x + ?)(x - ?)\)
What two numbers add up to 5 [from the middle term] and multiply together to equal -6? {6, -1}! So we plug these into the factors and we have:
\(\displaystyle (x+6)(x-1)\)
The completely factored formula looks like:
\(\displaystyle y = (x + 6)(x - 1)\)
Now to solve!
When you solve an equation, you set the y to 0, so
\(\displaystyle 0 = (x + 6)(x - 1)\)
Since you have the factors multiplying by eachother, you can split them apart and set them both to equal like:
\(\displaystyle 0 = (x + 6) and 0 = (x - 1)\)
Solve for x!
so the solution to the equation would be x={-6,1}!