Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 50a

Capitolo 2, Problema 50a

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is two more than the square of the x-value.

Guida verificata passo dopo passo

Step 1: Start by translating the English sentence into a mathematical equation. The sentence states that 'The y-value is two more than the square of the x-value.' This can be written as y = x^2 + 2.

Step 2: To graph the equation, recognize that this is a quadratic equation in the form y = x^2 + c, where c = 2. This represents a parabola that opens upwards and is shifted 2 units up from the standard parabola y = x^2.

Step 3: Create a table of values for x and calculate the corresponding y-values using the equation y = x^2 + 2. For example, choose x-values such as -2, -1, 0, 1, and 2, and compute their y-values.

Step 4: Plot the points from the table of values on a coordinate plane. For instance, if x = -2, y = (-2)^2 + 2 = 6, so plot the point (-2, 6). Repeat this for all chosen x-values.

Step 5: Connect the plotted points with a smooth curve to complete the graph of the parabola. Ensure the curve reflects the symmetry of the parabola about the y-axis.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form y = ax^2 + bx + c. In this context, the relationship between the variables x and y involves squaring the x-value, which indicates that the graph will be a parabola. Understanding the properties of parabolas, such as their vertex and direction of opening, is essential for graphing the equation accurately.

Video consigliato:

06:36

Solving Quadratic Equations Using The Quadratic Formula

Translating English Sentences to Equations

Translating English sentences into mathematical equations requires understanding the relationships described in the sentence. In this case, the phrase 'the y-value is two more than the square of the x-value' translates to the equation y = x^2 + 2. This skill is crucial for converting verbal descriptions into mathematical expressions that can be analyzed and graphed.

Video consigliato:

06:00

Categorizing Linear Equations

Graphing Equations

Graphing equations involves plotting points on a coordinate plane to visually represent the relationship between the variables. For the equation y = x^2 + 2, one would calculate y-values for various x-values and plot these points. Understanding how to interpret the graph, including identifying key features like intercepts and the shape of the curve, is vital for a complete analysis of the equation.

Video consigliato:

04:29

Graphing Equations of Two Variables by Plotting Points

Pratica correlata

Domanda del libro di testo

In Exercises 37–52, perform the indicated operations and write the result in standard form. (3√-5)(- 4√-12)

174

views

Domanda del libro di testo

Solve each equation in Exercises 47–64 by completing the square. $x^{2} - 6 x - 11 = 0$

965

views

Domanda del libro di testo

Perform the indicated operations and write the result in standard form. (7-i)(2+3i)

915

views

Domanda del libro di testo

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

774

views

Domanda del libro di testo

In Exercises 51–58, solve each compound inequality. 6 < x + 3 < 8

1161

views

Domanda del libro di testo

Solve each equation in Exercises 47–64 by completing the square. $x^{2} + 4 x = 12$

849

views