Quadratic Equation

A quadratic expression in one independent variable x is generally written as:

$a{x}^2+bx+c$

where a,b,c are constants, and 

$a\mathrm{\ne }0$

 (otherwise, the equation becomes linear). A quadratic equation is written as:

$a{x}^2+bx+c=0$

Would you like me to generate some self-assessment exercises on quadratic expressions and equations? Here are a few you can try:

Self-Assessment Exercises:

1. Solve the following quadratic equations using the quadratic formula:

   • $x^2-5x+6=0$
   • $2x^2+3x-2=0$

2. Factorize the following quadratic expressions:

   • $x^2-7x+12$
   • $3x^2-2x-8$

3. Find the roots of the quadratic equation by completing the square:

   • $x^2+4x-5=0$

4. For the quadratic function 

   $f(x)=2x^2-3x+4$

   determine:

   • The vertex

   • The axis of symmetry

   • Whether the parabola opens upwards or downwards