Quadratic Formula
In this lesson on the quadratic formula, students will learn how to solve quadratic equations of the form \(ax^2 + bx + c = 0\). The formula allows you to find the values of \(x\) by substituting the coefficients into a standard expression, and is useful to find solutions to quadratic equations where factorisation cannot work.
Related Lessons:
Recap: Completing The Square
This video revisits the earlier topic of Completing the Square. The quadratic formula is derived from this method and represents its final general form for solving quadratic equations.
\(x^2+nx+c=\left(x+\frac{n}{2}\right)^2-\left(\frac{n}{2}\right)^2+c\)
Proving Quadratic Formula
In this lesson, students will learn how the quadratic formula is derived by completing the square. Starting with a general quadratic equation, the expression is rearranged and transformed into a perfect square form. By isolating the variable and simplifying step by step, the quadratic formula is obtained. This process helps students understand where the formula comes from, rather than just memorising it.
For a quadratic equation of the form \(ax^2+bx+c=0\):
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
Students who prefer not to memorise the quadratic formula can instead use the Completing the Square method to solve quadratic equations.
Applying Quadratic Formula - 2 Examples
- \(5𝑥^2+7𝑥−11=0\)
- \(𝑥^2+11𝑥+8=0\)