Compare both method
In my general formula solution, I can observe a two solution type of quadratic equation. After having arranged the equation I identify the value for a, b and c. I then substitute these values inside my quadratic formula, and different things are inferred from here. Since the number inside the square root is positive, the quadratic formula has indeed a solution, since if it was the other way around, it would be impossible to calculate the square root of a negative number. No number multiplied by itself gives a negative outcome. Then, when having to do the plus minus sign operations, neither of the two x's gives 0 as a result, which means there are two solutions. If one of those numbers was a zero there would only be one real solution, and the answer would be the value of x repeated inside the key: {x1,x1}. Now, when observing the parabola, many other things can be inferred. Not only is the result the same as the one with general formula, but it is also exact, and therefore the amount of solutions is two. If the parabola intersects the x-axis twice, those two points will be the solution. If there is only one intersection (usually the vertex), there is only one solution and you do the same as with the quadratic formula, repeat the value for the x twice. If the parabola is not touching the x-axis, then it has no solution. The vertex is a maximum point, since the parabola goes downwards and it is found above the x-axis. If the parabola goes upwards, then the vertex would be a minimum point.