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Questions and Answers
Empareja los siguientes términos relacionados con polinomios:
Empareja los siguientes términos relacionados con polinomios:
Grado = La mayor potencia de la variable en la expresión Coeficiente principal = Coeficiente del término con la mayor potencia Término constante = Término en el polinomio que no contiene variable Variable = Símbolo que representa un número desconocido
Empareja los siguientes símbolos con su significado en desigualdades:
Empareja los siguientes símbolos con su significado en desigualdades:
= Mayor que < = Menor que ≤ = Menor o igual que ≠ = No es igual a
Empareja las funciones cuadráticas con sus características:
Empareja las funciones cuadráticas con sus características:
f(x) = ax² + bx + c = Forma general de una función cuadrática Parábola = Gráfica de una función cuadrática Vértice = Punto más alto o bajo de la parábola Ejes de simetría = Línea que divide la parábola en dos partes iguales
Empareja las formas de ecuaciones lineales con su definición:
Empareja las formas de ecuaciones lineales con su definición:
Empareja los términos con los métodos de factorización:
Empareja los términos con los métodos de factorización:
Empareja las propiedades de las desigualdades con sus descripciones:
Empareja las propiedades de las desigualdades con sus descripciones:
Empareja los métodos para encontrar el vértice de una función cuadrática:
Empareja los métodos para encontrar el vértice de una función cuadrática:
Empareja los tipos de ecuaciones lineales con sus características:
Empareja los tipos de ecuaciones lineales con sus características:
Study Notes
Polynomials
- Polynomials are algebraic expressions consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
- Examples of polynomials include: x² + 2x + 1, 3y³ - 5y + 7, and 8z.
- Key characteristics of polynomials include degree, leading coefficient, and constant term.
- The degree of a polynomial is the highest power of the variable in the expression.
- The leading coefficient is the coefficient of the term with the highest power of the variable.
- The constant term is the term in the polynomial that does not contain a variable.
Inequalities
- Inequalities represent a relationship between two expressions that are not necessarily equal.
- Symbols used to represent inequalities include: > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), ≠ (not equal to).
- Inequalities can be solved using algebraic methods similar to solving equations, but with the important consideration of flipping the inequality sign when multiplying or dividing by a negative number.
- Solutions to inequalities are often represented using intervals on a number line.
Quadratic Functions
- Quadratic functions are polynomial functions of degree 2.
- Their general form is f(x) = ax² + bx + c, where 'a', 'b', and 'c' are constants and 'a'≠0.
- The graph of a quadratic function is a parabola.
- Key features of parabolas include vertex, axis of symmetry, and x-intercepts (roots or solutions).
- Methods for finding the vertex include completing the square, the vertex formula (-b/2a), and graphing.
Linear Equations
- Linear equations represent a relationship between two variables that, when graphed, form a straight line.
- The general form of a linear equation is Ax + By = C (standard form) or y = mx + b (slope-intercept form), where 'm' is the slope and 'b' is the y-intercept.
- The slope of a line represents the rate of change between two variables.
- Solutions to linear equations are pairs of values (x, y) that satisfy the equation. These solutions can be found graphically or algebraically.
- Systems of linear equations can be solved using graphical methods (intersection of lines), substitution, or elimination.
Factoring Techniques
- Factoring involves rewriting an expression as a product of its factors.
- Common factoring involves identifying common factors in all terms.
- Difference of squares is a special factoring technique for expressions that follow the pattern a² – b² = (a – b)(a + b).
- Trinomial factoring involves factoring expressions of the form ax² + bx + c. Techniques like grouping or trial-and-error can be used.
- Grouping is a useful technique for factoring polynomials with four or more terms.
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