Welcome to the bonus round of quadratic equations. We have now reached the end of this chapter. Today, it is time to set back and relax. In this video, we will look at the daily life occurrences of quadratic equations and also discuss what happens when the discriminant is negative. Our understanding of graphs of a quadratic equation will help us in finding them in our daily lives. I am sure you all have watched the game of golf. The path of the ball when it is hit, what shape does it remind you of? Indeed, a parabola. This type of motion, the motion that a golf ball executes is called as a projectile motion. The understanding of this type of motion helps us to launch satellite in space and more. In olden times, they used to fire cannon balls on the enemy castles and the guards in the enemy castles also used to fire cannon balls on their rivals. This has a large application on projectile motion. We know that the path of a projectile is called as a parabola and thus the equation of a path will be a quadratic equation. Two out of the three kinematic equations are quadratic. As you can see on the screen, the above one is a quadratic equation and the below one is not a quadratic equation. Let us look at the graph of these equations. We can see through the graph that these equations are very useful in modeling the motion in the real world synonyms. You will study more about this in your physics class. Till now, while solving the quadratic equations, if we got a negative quantity inside the discriminant, we would leave the equation and happily claim that there are no real roots. But no more. Let us now define the quantity root of minus 1 as i, i for imaginary. So root of minus 1 equals i, i square equals minus 1, i cube equals minus i, i raise to 4 equals 1. Thus we see that i plus i square plus i cube plus i raise to 4 equals 0. If there can be imaginary numbers, there surely can be some imaginary mathematics associated with them. There are a lot of interesting things arising from quadratic equations. Hope you enjoyed a graphical method towards quadratic equations. Stay tuned, meet you in the next chapter.