Quadratic Equation
\[x = {-b \pm \sqrt{b^2-4ac} \over 2a}\]
- Used to solve quadratic equations
- Derived from the process of completing the square
- Example: For the equation \(2x^2 - 3x + 1 = 0\), the roots can be found using the quadratic formula
Pythagorean Theorem
\[a^2 + b^2 = c^2\]
- Used to calculate the length of the sides in a right triangle
- Named after the ancient Greek mathematician Pythagoras
- Example: For a right triangle with sides of lengths 3 and 4, the length of the hypotenuse is 5
Newton's Second Law
\[F = ma\]
- States that the force applied to a body produces a proportional acceleration
- The relationship between an object's mass m, its acceleration a, and the applied force F
- Example: If a force of 10 N is applied to a 2 kg object, the acceleration of the object is 5 m/s^2
Einstein's Theory of Relativity
\[E = mc^2\]
- States that energy (E) is equal to mass (m) times the speed of light (c) squared
- One of the most famous equations in physics
- Example: The energy of a 1 kg object is approximately \(9 \times 10^{16}\) joules