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Hi, this is Presh Talwalkar Quadratic equations are extremely important in mathematics But unfortunately they can also be very confusing In this video Im going to present a visual and geometric proof so that you understand the quadratic formula intuitively. Imagine you want to solve x^2 + 2x -15 = 0 You could solve this by graphing the equation x^2 + 2x -15 The point at which the graph crosses the x axes are the solutions. You could also solve this equation by factoring into linear terms If you set these linear terms equal to zero, you get the same solutions as written in the graph. When those methods dont work The quadratic formula will always tell you how you can solve any quadratic equations with arbitrary constants a, b and c. So this is a very useful formula But unforunately, its not often presented in an intuitive way. Why exactly does it work ? So lets try and understand this geometrically. Lets solve this equation First well add 15 to both sides so that we have x^2+2x=15