Standard form	[[$ ax^2+bx+c=0, \quad a\neq 1 $]]
Quadratic formula:	[[$ \quad x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} $]]​

Parabola opening direction and shape:

• If [[$ a > 0 $]], the parabola opens upwards. 
• If [[$ a < 0 $]], the parabola opens downwards. 
• If [[$ |a| $]] is small, the parabola is wide. 
• If [[$ |a| $]] is great, the parabola is narrow.

Incomplete quadratic equations

The number of solutions to equation [[$ ax^2 + c = 0 $]] depends on the constant [[$c$]]:

• [[$c < 0$]]: two solutions, solutions of opposite numbers 
• [[$c= 0$]]: the only solution is [[$x = 0$]]
• [[$c > 0$]]: no solution 

Solutions of the equation [[$ ax^2 + bx = 0 $]]:

• always two solutions, the other is always [[$x = 0$]].