Key Equations

College Algebra with Corequisite Support 2eKey Equations

Key Equations

quadratic formula

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

Distance

d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}

Slope of a line

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

Point-Slope equation of a line

y - y_{1} = m (x - x_{1})

Adding Complex Numbers

(a + b i) + (c + d i) = (a + c) + (b + d) i

Subtracting Complex Numbers

(a + b i) - (c + d i) = (a - c) + (b - d) i

Square Root Property

If x^{2} = k then x = \pm \sqrt{k}

Quadratic Formula

If a x^{2} + b x + c = 0 then x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Rational Exponents

a^{\frac{m}{n}} = {(a^{\frac{1}{n}})}^{m} = {(a^{m})}^{\frac{1}{m}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}

Absolute Value

If x \geq 0, | x | = x; If x < 0, | x | = - x

Addition Property of Inequalities

If a < b then a + c < b + c

Multiplication Property of Inequalities

\begin{matrix} If a < b and c > 0, then a c < b c \\ If a < b and c < 0, then a c > b c \end{matrix}

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- Authors: Jay Abramson, Sharon North
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- Book title: College Algebra with Corequisite Support 2e
- Publication date: Dec 21, 2021
- Location: Houston, Texas
- Book URL: https://openstax.org/books/college-algebra-corequisite-support-2e/pages/1-introduction-to-prerequisites
- Section URL: https://openstax.org/books/college-algebra-corequisite-support-2e/pages/2-key-equations

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