If the quadratic equation can be used to determine when a function equals zero, is there a modified quadratic equation that can determine when a function equals another constant?
Any time you want to find for what value of
We will start by setting the general quadratic function equal to
Now we divide by
At this point we need to complete the square. Here is an explanation of what that means. We add
Now the left hand side is in a form that can be simplified into a "neat" square.
At this point we want a common denominator on the right hand side in order to combine both fractions together. Multiply the first fraction by
I rearranged the right hand side a little bit in order to make it look more like the original quadratic equation. We can now take the square root of both sides.
Lastly, move the constant term from the left to the right by subtracting from both sides.
There you have it, the only difference from the original quadratic formula is that the