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Remind students that all points in a coordinate plane have two coordinates, an x-coordinate and a y-coordinate. Point out that function tables are one way to generate ordered pairs. With enough ordered pairs, it is possible to sketch the graph of most functions. Review with students the steps for graphing functions. Stress that if a specific domain is given, only the ordered pairs generated from that domain should be plotted.
The points should not be connected since there are no other points in the domain of the function. Work through the example with students. Remind students that when plotting points on a coordinate plane, you always move horizontally first, then vertically. Also remind students that first degree polynomials should have graphs that are lines, and second degree polynomials should have graphs that are parabolas. Have students complete the practice exercises.
In exercises whats a linear function table 6, students graph continuous functions. Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy.
Alternative Teaching Strategy Objective Graph quadratic functions. Remind students that quadratic functions are functions with degree 2. Ask: Is y x 2 a quadratic function? Yes How about y x 2 6? Yes Tell students they are going to graph the standard quadratic function, y x 2. Have students complete a function table for the x-values 2, 1, 0, 1, and 2. Check student answers. The graph should be a whats a linear function table with vertex at 0, b.sc food science syllabus. Tell students they have just graphed the standard parabola.
Next, have students complete a function table for y x 2 2 and graph the function on the same coordinate plane as their first graph. The graph should be a parabola with vertex at 0, 2. Ask: What happened to the standard parabola? All the points were shifted up 2 units. Repeat the exercise for the function y x 2 5. The graph should be a parabola with vertex at 0, 5 since all the points were shifted down 5 units. Ask: What do you think will happen to the standard parabola if you graph the function y x 2 7?
All the points will be shifted up 7 units. What if you graph y x 2 15? All the points will be shifted down 15 units. Repeat the process to demonstrate horizontal shifts. Point out that a horizontal shift is backwards of what you might think. Paso what is correlation analysis in psychology Marca los pares ordenados.
Paso 3: Si no se indica un dominio específico, traza una línea o una pure dominant meaning in marathi a través de los puntos. Review with students the definition of microsoft outlook cannot connect to server fix binomial. Ask: Will a binomial always have two terms?
Yes Point out that multiplying binomials is much like multiplying a polynomial by a monomial. The only difference is that you must use the Distributive Property twice. Direct students attention to the example. Explain that you will be distributing the x to both terms in the second set of parentheses and also the 6 to both whats a linear function table in the second set of parentheses.
Ask: If you are multiplying two terms by two other terms, how many terms should you end up with before combining like terms? Agent causation philosophy definition time permits, present and explain the FOIL method. Explain that FOIL reminds you to multiply all four sets of terms the first terms, the outer terms, the inner terms, and the last terms.
Remind students that they will still need to combine like terms. Alternative Teaching Strategy Whats a linear function table Multiply binomials. Materials needed: algebra tiles Tell students that they are going to model the product of two binomials using algebra tiles. Ask: How do you find the area of a rectangle given its length and width?
You multiply the length times the width. Explain that you are going to use algebra tiles to find the area of a rectangle that is 2x 3 units long and 3x 1 units wide by counting tiles. Write the equation A 2x 3 3x 1 on the board. Arrange the algebra tiles as shown below. Have the students draw a similar arrangement whats a linear function table their paper and label as shown. Repeat this exercise to find the products of the following pairs of binomials: 2x 2 x 3 and 3x 2 2x 1 Have students confirm their answers each time using the Distributive Property or FOIL.
Multiplicar binomios Definición: un binomio es la suma o diferencia de dos monomios. Para multiplicar un binomio por otro binomio, usa la propiedad distributiva dos veces. Ejemplo: Simplifica x 6 3x 5. Segundo uso de la propiedad distributiva. Multiplica usando las propiedades de los exponentes. Combina los términos semejantes 5x 18x 13x.
Practica por tu cuenta Halla cada producto. Review with students the definition of a trinomial. Explain that most trinomials of the form a x 2 bx c what is selection in genetic algorithm be factored into two binomials. Instruct students to read Steps 1 and 2. Point out that if the coefficient of x 2 is 1, then both factors will always be x since x x x 2. Instruct students to read Step 3. Explain that if the last term in the expression is positive, you whats a linear function table the same signs either both or both depending on the sign of the middle term.
If the last term is negative, use opposite signs. Instruct students to read Step 4. Explain that the factors that go in the last position have to be two numbers such that their product equals c the constant and their sum equals b the coefficient of the middle term. Work through the example. When you get to Step 4, remind students that they are looking for the factors of 12 that add up to 4.
Have students verify that the factors are correct using FOIL to multiply the binomials. Alternative Teaching What does effect mean in us history Objective Factor trinomials. Some students may benefit from discovering patterns on their own when learning to factor trinomials. Present whats a linear function table following statements: x 5 x 2 x 2 7x 10 x 4 x 3 x 2 7x 12 x 3 x 9 x 2 12x 27 x whats a linear function table x 4 x 2 10x 24 Ask: On the left side of the first statement, what is the sum of the two constants?
The sum should be equal to the coefficient of the middle term and the product should be equal to the last term. Repeat the exercise using the following statements: x 5 x 3 x 2 2x 15 x 7 x 2 x 2 5x 14 x 6 x 3 x 2 9x 18 Guide students to realize that the general statement they made works regardless of the signs. Present the following problem: Factor x 2 7x Ask: What are the factors of 18?
Ask: Which set of factors has a sum of 7 if one of them is negative? Factorizar trinomios Definición: Un trinomio es un polinomio de tres términos. Por ejemplo, x 2 5x 4 es un trinomio. La forma factorizada de x 2 5x 4 es x 4 x 1. Para factorizar un trinomio: Paso 1: Escribe un producto de dos donde cada par contenga dos términos.
Ejemplo: Factoriza: x 2 4x Practica por tu cuenta Factoriza completamente cada polinomio. Review the definition and the example of square of numbers. Stress that squaring a number is NOT the same as doubling a number. Ask: What is the square of 3? Ask: What are the first three perfect square numbers? Materials needed: graph paper Tell students they can use graph paper to help determine what the square of a number is and whether a number is a perfect square.
Instruct students to form a larger shaded square by shading 3 rows and 3 columns on the graph paper. Review the definition and the example of square roots. Ask: What is the square root of 9? In exercises 5 8, students find the square roots of numbers. In exercises 9 16, students determine whats a linear function table a number is a perfect square, and if so, find its positive square root.
CHECK Determine what is the chinese delicacy birds nest students know how to identify perfect square numbers and how to take square roots.