As the final blog post of Math-11, I am doing a top 5 list of things that I learned this year.
- Solving with quadratic formula
- Sine & Cosine law
- Solving by completing square (& vertex form)
- Discriminant
- Entire radicals to mixed
Explanation
The quadratic formula provides a straightforward method for solving any quadratic equation regardless of whether the roots are real or complex. Unlike factoring or completing the square, which may not always be easy or possible, the quadratic formula works in all cases where a, b, and c are known.
The Sine and Cosine Laws are essential for solving non-right triangles, which frequently occur in real-world problems, such as engineering, navigation, and physics.
Completing the square is (usually) a fast way to solve/simplify and it provides insight into the visual representation of quadratic equations (vertex form).
The discriminant tells us the nature of the roots of a quadratic equation (real and unequal, real and equal, or complex/non-real).
Converting entire radicals to mixed radicals simplifies expressions and makes them easier to work with, especially in algebraic operations.