This section explores the process for sketching graphs of polynomial equations when their solutions have been identified.
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This section explores logarithms as operations that are the inverse of exponents. It investigates the process for "undoing" or "eliminating" variable exponents when solving exponential equations.
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"Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)
"Los estudiantes conectan la aritmética polinomial con los cálculos con números enteros e enteros. Los estudiantes aprenden que la aritmética de las expresiones racionales se rige por las mismas reglas que la aritmética de los números racionales. Esta unidad ayuda a los estudiantes a ver conexiones entre soluciones a ecuaciones polinomiales, ceros de polinomiales,, y gráficos de funciones polinómicas. Las ecuaciones polinomiales se resuelven sobre el conjunto de números complejos, lo que lleva a una comprensión inicial del teorema fundamental del álgebra. Los problemas de aplicación y modelado conectan múltiples representaciones e incluyen situaciones de mundo real y puramente matemáticas.
Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.
English Description:
"Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)
En módulos anteriores, los estudiantes analizan el proceso de resolver ecuaciones y desarrollar fluidez en la escritura, interpretación y traducción entre varias formas de ecuaciones lineales (Módulo 1) y funciones lineales y exponenciales (Módulo 3). Estas experiencias combinadas con el modelado con datos (Módulo 2), preparan el escenario para el módulo 4. Aquí los estudiantes continúan interpretando expresiones, crean ecuaciones, reescriben ecuaciones y funciones en formas diferentes pero equivalentes, y gráficos e interpretan funciones, pero esta vez utilizando polinomial funciones y funciones más específicamente cuadráticas, así como funciones de raíz de raíz cuadrada y de cubos.
Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.
English Description:
In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
Use a number line to graph inequalities
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Learn how to express inequalities using various notation and by graphing.
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Learn how to graph linear equations by finding intercepts using substitution.
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This site from Richland Community College provides lecture notes to a class on Algebra. It covers a wide array of topics including functions, quadratic equations, inequalities, and much more.
Solve single variable addition and subtraction equations by using mental math
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Learn how to use the midpoint formula.
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In this lesson students solve equations that involve more than two steps to isolate the variable. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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In this lesson students combine terms that contain the same variable to solve equations. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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In this lesson students solve equations by combining like terms. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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In this lesson students learn how to solve multi-step equations by combining like terms. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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This lesson covers vertex, intercept, and standard forms. Here you'll explore the different forms of the quadratic equation.
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Learn how to solve problems involving rates of change.
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This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.
Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.
Express large and small numbers using scientific notation.
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