# Comments:LaTeX-code for the most common formulas

If you have somewhere a very long formula, please share it with us. This will save time for everybody! Just edit this page and paste you code at inside the input-box, if you don't know how to use the wiki-code correctly.

## How to use the formulas

Just copy the text from the column LaTex Input into your text-object input-box. If the formula should be dynamic you need to insert the object instead of the variables that are used here.

## Preview

Check how they look in Java (http://www.geogebra.org/student/m33487?mobile=false) and HTML5 (http://www.geogebra.org/student/m33487?mobile=true)

## Useful Formulas

Usage LaTex Input LaTex Output
Square-root symbol \sqrt{x} \sqrt{x}
Fractions \frac{a}{b+c} \frac{a}{b+c}
\left( and \right) for large brackets \left( \frac{a}{b} \right) ^{2} \left( \frac{a}{b} \right) ^{2}
Use \textcolor for color x^{\textcolor{#FF00FF}{2}}
Use \cr for a line break x=3 \cr y=2 \begin{array} x x=3 \\ y=2 \end{array}
Use \text{ } to mix text and expressions \text{The quadratic formula is }x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} \text{The quadratic formula is }x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}
Slope for a straight line m=\frac{y_2-y_1}{x_2-x_1} m=\frac{y_2-y_1}{x_2-x_1}
Slope for a straight line (2) m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B} m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B}
Compound Interest Amount = Principal \cdot \left( 1 + \frac {rate}{periods} \right) ^ {time\; \cdot\; periods} Amount = Principal \cdot \left( 1 + \frac {rate}{periods} \right) ^ {time\; \cdot\; periods}
Quadratic Equation a x^2\; +\; b x\; +\; c\; =\; 0 a x^2\; +\; b x\; +\; c\; =\; 0
Simplified Quadratic Equation x^2\; +\; p x\; +\; q\; =\; 0 x^2\; +\; p x\; +\; q\; =\; 0
Vertex Form f(x)\; =\; a(x\; -\; h)^2\; +\; k f(x)\; =\; a(x\; -\; h)^2\; +\; k
Factored Form f(x)\; =\; (x\; +\; a)\;(x\; +\; b) f(x)\; =\; (x\; +\; a)\;(x\; +\; b)
Quadratic Formula x\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a} x\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a}
Quadratic Formula x_{1/2}\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a} x_{1/2}\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a}
Quadratic Formula for Simplified Quadratic Equation x_{1/2}\; =\; - \frac{p}{2}{\; \pm\; \sqrt {\left( \frac{p}{2} \right)^2\; -\; q}} x_{1/2}\; =\; - \frac{p}{2}{\; \pm\; \sqrt {\left( \frac{p}{2} \right)^2\; -\; q}}
Quadratic Formula for Simplified Quadratic Equation x_{1/2}\; =\; - \frac{p}{2}{\; \pm\; \sqrt {\left( \frac{p}{2} \right)^2\; -\; q}} x_{1/2}\; =\; - \frac{p}{2}{\; \pm\; \sqrt { \frac{p^2}{4} \; -\; q}}
Cubic Equation a x^3\; +\; b x^2\; +\; c x\; +\; d\; =\; 0 a x^3\; +\; b x^2\; +\; c x\; +\; d\; =\; 0
Basic Trigonometry Forms \sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c) \sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)
f(x)\; =\; a\; \sin\; b\;(x\; -\; h)\; +\; k f(x)\; =\; a\; \sin\; b\;(x\; -\; h)\; +\; k
f(x)\; =\; a\; sin\; (B x + C) + k f(x)\; =\; a\; \sin\; (B x + C) + k
b\;(x\; -\; h)\; = B\; \left( x\; -\; \frac {-C}{B} \right) b\;(x\; -\; h)\; = B\; \left( x\; -\; \frac {-C}{B} \right)
h\; = \frac {-C}{B} h\; = \frac {-C}{B}
Limit (corrected to work in HTML5 as well as Java) \lim_{x \to \infty} \left( \frac{1}{x} \right) \lim_{x \to \infty} \left( \frac{1}{x} \right)
Distance Formula \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}
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