A quadratic expression or equation is a polynomial of degree 2 (highest power of variable is 2).
Standard form: ax^2+bx+c where a, b and c are constants.
If ax^2+bx+c=0, solution can be found using formula: x=(-b±√(b^2-4ac))/2a which can be derived by completing the square:
x^2+bx/a+c/a=0; x^2+bx/a=-c/a; x^2+bx/a+b^2/4a^2=b^2/4a^2-c/a; (x+b/2a)^2=b^2/4a^2-c/a.
Square root each side: x+b/2a=±√(b^2/4a^2-c/a)=±√(b^2-4ac)/2a.
x=(-b±√(b^2-4ac))/2a.
Graph of a quadratic is a parabola (y=ax^2+bx+c) which resembles a U shape with broadening arms when a is positive. It can also be an upside down U (a is negative). The vertex is the lowest or highest point on the curve. Parabola can also be lying on its side: x=ay^2+by+c where y is the vertical axis and x the horizontal axis.