Quadratic Equation

1. quadratic equations

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

where $a, b, c$a,b,c are constants, and $a \neq 0$a=0 (otherwise, the equation becomes linear). A quadratic equation is written as:

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:

   • $x^2 - 5x + 6 = 0$x2−5x+6=0

   • $2x^2 + 3x - 2 = 0$2x2+3x−2=0

2. Factorize the following quadratic expressions:

   • $x^2 - 7x + 12$x2−7x+12

   • $3x^2 - 2x - 8$3x2−2x−8

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

   • $x^2 + 4x - 5 = 0$x2+4x−5=0

4. For the quadratic function $f(x) = 2x^2 - 3x + 4$f(x)=2x2−3x+4, determine:

   • The vertex

   • The axis of symmetry

   • Whether the parabola opens upwards or downwards