Mathedemo

Math in TeX notation

When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ $$ \begin{array}{rcll} y & = & x^{2}+bx+c\\ & = & x^{2}+2\times\dfrac{b}{2}x+c\\ & = & \underbrace{x^{2}+2\times\dfrac{b}{2}x+\left(\frac{b}{2}\right)^{2}}- {\left(\dfrac{b}{2}\right)^{2}+c}\\ & & \qquad\left(x+{\dfrac{b}{2}}\right)^{2}\\ & = & \left(x+\dfrac{b}{2}\right)^{2}-\left(\dfrac{b}{2}\right)^{2}+c & \left|+\left({\dfrac{b}{2}}\right)^{2}-c\right.\\ y+\left(\dfrac{b}{2}\right)^{2}-c & = & \left(x+ \dfrac{b}{2}\right)^{2} & \left|\strut(\textrm{vertex form})\right.\\ y-y_{S} & = & (x-x_{S})^{2}\\ S(x_{S};y_{S}) & \,\textrm{or}\, & S\left(-\dfrac{b}{2};\,\left(\dfrac{b}{2}\right)^{2}-c\right) \end{array} $$

Math in MathML notation

When

a \neq 0

, there are two solutions to

a x^{2} + b x + c = 0

and they are

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} .

LaTeX in HTML