Textbook Question
The graph of a quadratic function is given. Write the function's equation, selecting from the following options.
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Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 4, Problem 7
Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.
Verified step by step guidance1
Identify the type of variation described: since y varies jointly as x and z, we write the equation as \(y = k \cdot x \cdot z\), where \(k\) is the constant of proportionality.
Use the given values \(y = 25\), \(x = 2\), and \(z = 5\) to find the constant \(k\). Substitute these into the equation: \(25 = k \cdot 2 \cdot 5\).
Solve for \(k\) by isolating it on one side: \(k = \frac{25}{2 \cdot 5}\).
Write the general formula for \(y\) using the found value of \(k\): \(y = k \cdot x \cdot z\).
Substitute the new values \(x = 8\) and \(z = 12\) into the formula to find the new value of \(y\): \(y = k \cdot 8 \cdot 12\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Joint Variation
Joint variation describes a relationship where a variable depends on the product of two or more other variables. In this problem, y varies jointly as x and z means y = kxz, where k is a constant. Understanding this helps set up the correct equation to find unknown values.
Finding the Constant of Variation
To solve variation problems, first find the constant k by substituting known values of the variables into the joint variation equation. Here, using y = 25, x = 2, and z = 5 allows calculation of k, which is essential for determining y under new conditions.
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Finding the Domain of an Equation
Applying the Four-Step Procedure for Variation Problems
The four-step procedure typically involves identifying the variation type, writing the equation, finding the constant, and solving for the unknown. Following these steps systematically ensures accurate solutions in variation problems like this one.
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Related Practice
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