On November 12, 2025, Google replaced its homepage logo in India with an animated doodle celebrating the quadratic equation (ax^2 + bx + c = 0). The illustration shows a curved path symbolising the way this formula describes parabolic motion in physics and engineering. The quadratic equation remains one of the most-searched formulas online. Google notes that it appears in fields ranging from engineering to economics and even sports. For example, the doodle uses the motion of a basketball shot to demonstrate how a falling object follows a parabola, which the equation models.
In algebraic terms the equation is written as (ax^2 + bx + c = 0), where (a), (b), and (c) are constants and (a) cannot be zero. The solutions for (x) are given by the quadratic formula (x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}). Whether the solutions are real or complex depends on the discriminant ((b^2 – 4ac)). The history of this formula stretches back to ancient civilisation. Mathematicians in India and elsewhere analysed such relations centuries ago. One key figure, Brahmagupta, formulated general methods in the seventh century that correspond to modern algebraic solutions.
In practical use the equation allows engineers and physicists to calculate peak heights, trajectories and landing positions of moving objects. For instance a ball thrown in the air rises, then falls in a path a quadratic equation can predict. Civil engineers apply the same underlying math when designing arches, bridges or motion-controlled mechanisms. Even in business the formula helps model cost-profit relationships and optimisation problems.
By choosing this theme for its doodle Google aligns the timing with educational calendars. Many students encounter the quadratic equation in high-school syllabus around October-November. The doodle turns a search-engine moment into an interactive learning opportunity: clicking it brings up detailed explanations and searches related to the equation. In short this doodle does more than mark a mathematical milestone. It reminds users that behind everyday curves and motion lies algebraic logic. From playgrounds to physics labs, the quadratic equation connects ideas and reality. This moment turns the homepage into a tiny classroom, inviting anyone curious to explore the formula that quietly shapes so much of our world.
