A quadratic equation is a type of polynomial equation of degree 2. It has the general form:
ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0
where:
- xxx is the variable,
- aaa, bbb, and ccc are constants,
- a≠0a\neq 0a=0 (because if a=0a=0a=0, then it would not be quadratic, but linear).
Key points about quadratic equations:
- The highest power of the variable xxx is 2.
- The graph of a quadratic equation is a parabola.
- The parabola opens upwards if a>0a>0a>0 and downwards if a<0a<0a<0.
How to solve a quadratic equation?
You can solve it by:
- Factoring (if possible),
- Using the quadratic formula :
x=−b±b2−4ac2ax=\frac{-b\pm \sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac
- Completing the square ,
- Graphically (finding where the parabola crosses the x-axis).
If you want, I can explain any of these methods in detail!
