College Algebra
College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Chapter 3, Problem 11RE

Using Standard Form to Graph a Parabola In Exercises 3-14, write the quadratic function in standard form and sketch its graph. Identify the vertex, axis of symmetry, and x -intercept s .

h ( x ) = 4 x 2 + 4 x + 13

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Writing the Equation of a Parabola in Standard Form In Exercises 39-44, write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result. 39. Vertex: (-2, 5); 40. Vertex: (4, 1); 41. Vertex: (1, -2): Point: (0,9) Point: (6, -7) Point: (-1, 14)
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Chapter 3 Solutions

College Algebra

Ch. 3.1 - Sketch the graph of each quadratic function and...Ch. 3.1 - Prob. 2ECPCh. 3.1 - Sketch the graph of f(x)=x24x+3. Identify the...Ch. 3.1 - Write the standard form of the quadratic function...Ch. 3.1 - Rework Example 5 when the path of the baseball is...Ch. 3.1 - Prob. 1ECh. 3.1 - Fill in the blanks. A polynomial function of x...Ch. 3.1 - Fill in the blanks. A function is a second-degree...Ch. 3.1 - Fill in the blanks. When the graph of a quadratic...Ch. 3.1 - In Exercises 5-8, match the quadratic function...
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In Exercises 83-86, determine...Ch. 3.3 - True or False? In Exercises 83-86, determine...Ch. 3.3 - True or False? In Exercises 83-86, determine...Ch. 3.3 - Prob. 86ECh. 3.3 - Think About It In Exercises 87 and 88, perform the...Ch. 3.3 - Think About It In Exercises 87 and 88, perform the...Ch. 3.3 - Error Analysis Describe the error. Use synthetic...Ch. 3.3 - HOW DO YOU SEE IT? The graph below shows a...Ch. 3.3 - Exploration In Exercises 91 and 92, find the...Ch. 3.3 - Exploration In Exercises 91 and 92, find the...Ch. 3.3 - Think About It Find the value of k such that x4is...Ch. 3.4 - Determine the number of zeros of the polynomial...Ch. 3.4 - Prob. 2ECPCh. 3.4 - Prob. 3ECPCh. 3.4 - Find the rational zeros of fx=2x3+x213x+6.Ch. 3.4 - Find all real solutions of 2x35x2+15x+18=0.Ch. 3.4 - Find a fourth-degree polynomial function f with...Ch. 3.4 - Find the quartic (fourth-degree) polynomial...Ch. 3.4 - Prob. 8ECPCh. 3.4 - Prob. 9ECPCh. 3.4 - Prob. 10ECPCh. 3.4 - Find all real zeros of fx=8x34x2+6x3.Ch. 3.4 - Prob. 12ECPCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Zeros of Polynomial Functions In Exercises 9-14,...Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Zeros of Polynomial Functions In Exercises 9-14,...Ch. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - 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Prob. 67ECh. 3.4 - Finding the Zeros of a Polynomial Function In...Ch. 3.4 - Prob. 69ECh. 3.4 - Finding the Zeros of a Polynomial Function In...Ch. 3.4 - Finding the Zeros of a Polynomial Function In...Ch. 3.4 - Finding the Zeros of a Polynomial Function In...Ch. 3.4 - Prob. 73ECh. 3.4 - Finding the Zeros of a Polynomial Function In...Ch. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Using Descartes’s Rule of Signs In Exercises...Ch. 3.4 - Prob. 81ECh. 3.4 - Using Descartes’s Rule of Signs In Exercises...Ch. 3.4 - Prob. 83ECh. 3.4 - Using Descartes’s Rule of Signs In Exercises...Ch. 3.4 - Prob. 85ECh. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - Prob. 89ECh. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3.4 - Prob. 94ECh. 3.4 - Prob. 95ECh. 3.4 - Prob. 96ECh. 3.4 - Prob. 97ECh. 3.4 - Prob. 98ECh. 3.4 - Prob. 99ECh. 3.4 - Prob. 100ECh. 3.4 - Prob. 101ECh. 3.4 - Prob. 102ECh. 3.4 - Geometry You want to make an open box from a...Ch. 3.4 - Geometry A rectangular package to be sent by a...Ch. 3.4 - Prob. 105ECh. 3.4 - Prob. 106ECh. 3.4 - Prob. 107ECh. 3.4 - Prob. 108ECh. 3.4 - Prob. 109ECh. 3.4 - Prob. 110ECh. 3.4 - Prob. 111ECh. 3.4 - Prob. 112ECh. 3.4 - Prob. 113ECh. 3.4 - Prob. 114ECh. 3.4 - Prob. 115ECh. 3.4 - Think About It Sketch the graph of a fifth-degree...Ch. 3.4 - Writing an Equation In Exercises 117 and 118, the...Ch. 3.4 - Prob. 118ECh. 3.4 - Prob. 119ECh. 3.4 - Prob. 120ECh. 3.4 - Prob. 121ECh. 3.4 - Prob. 122ECh. 3.4 - Prob. 123ECh. 3.5 - The ordered pairs below give the median sales...Ch. 3.5 - Prob. 2ECPCh. 3.5 - The simple interest on an investment is directly...Ch. 3.5 - Neglecting air resistance, the distance s an...Ch. 3.5 - Prob. 5ECPCh. 3.5 - The resistance of a copper wire carrying an...Ch. 3.5 - The kinetic energy E of an object varies jointly...Ch. 3.5 - Fill in the blanks. Two techniques for fitting...Ch. 3.5 - Fill in the blanks. Statisticians use a measure...Ch. 3.5 - Fill in the blanks. The linear model with the...Ch. 3.5 - Fill in the blanks. An r-value, or, of a set of...Ch. 3.5 - Fill in the blanks. The direct variation model...Ch. 3.5 - Fill in the blanks. The mathematical model y=2xis...Ch. 3.5 - Fill in the blanks. Mathematical models that...Ch. 3.5 - Fill in the blanks. The joint variation model...Ch. 3.5 - Mathematical Models In Exercises 9 and 10, (a)...Ch. 3.5 - Mathematical Models In Exercises 9 and 10, (a)...Ch. 3.5 - Sketching a Line In Exercises 11-16, sketch the...Ch. 3.5 - Prob. 12ECh. 3.5 - Sketching a Line In Exercises 11-16, sketch the...Ch. 3.5 - Sketching a Line In Exercises 11-16, sketch the...Ch. 3.5 - Sketching a Line In Exercises 11-16, sketch the...Ch. 3.5 - Sketching a Line In Exercises 11-16, sketch the...Ch. 3.5 - Sports The ordered pairs below give the winning...Ch. 3.5 - Broadway The ordered pairs below give the starting...Ch. 3.5 - Direct Variation In Exercises 19-24, find a direct...Ch. 3.5 - Prob. 20ECh. 3.5 - Direct Variation In Exercises 19-24, find a direct...Ch. 3.5 - Prob. 22ECh. 3.5 - Direct Variation In Exercises 19-24, find a direct...Ch. 3.5 - Direct Variation In Exercises 19-24, find a direct...Ch. 3.5 - Direct Variation as an nthPower In Exercises...Ch. 3.5 - Prob. 26ECh. 3.5 - Direct Variation as an nthPower In Exercises...Ch. 3.5 - Direct Variation as an nthPower In Exercises...Ch. 3.5 - Inverse Variation as an nth Power In Exercises...Ch. 3.5 - Prob. 30ECh. 3.5 - Inverse Variation as an nth Power In Exercises...Ch. 3.5 - Prob. 32ECh. 3.5 - Think About It In Exercises 33 and 34, use the...Ch. 3.5 - Think About It In Exercises 33 and 34, use the...Ch. 3.5 - Determining Variation In Exercises 35-38,...Ch. 3.5 - Prob. 36ECh. 3.5 - Determining Variation In Exercises 35-38,...Ch. 3.5 - Determining Variation In Exercises 35-38,...Ch. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Prob. 40ECh. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Prob. 42ECh. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Prob. 44ECh. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Prob. 46ECh. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Finding a Mathematical Model In Exercises 39-48,...Ch. 3.5 - Describing a Formula In Exercises 49-52, use...Ch. 3.5 - Prob. 50ECh. 3.5 - Describing a Formula In Exercises 49-52, use...Ch. 3.5 - Describing a Formula In Exercises 49-52, use...Ch. 3.5 - Finding a Mathematical Model In Exercises 53-60,...Ch. 3.5 - Prob. 54ECh. 3.5 - Finding a Mathematical Model In Exercises 53-60,...Ch. 3.5 - Prob. 56ECh. 3.5 - Finding a Mathematical Model In Exercises 53-60,...Ch. 3.5 - Prob. 58ECh. 3.5 - Finding a Mathematical Model In Exercises 53-60,...Ch. 3.5 - Prob. 60ECh. 3.5 - Simple Interest The simple interest on an...Ch. 3.5 - Prob. 62ECh. 3.5 - Measurement Use the fact that 13 inches is...Ch. 3.5 - Measurement Use the fact that 14 gallons is...Ch. 3.5 - Hooke’s Law In Exercises 65-68, use Hooke’s Law,...Ch. 3.5 - Hooke’s Law In Exercises 65-68, use Hooke’s Law,...Ch. 3.5 - Hooke’s Law In Exercises 65-68, use Hooke’s Law,...Ch. 3.5 - Hooke’s Law In Exercises 65-68, use Hooke’s Law,...Ch. 3.5 - Ecology The diameter of the largest particle that...Ch. 3.5 - Work The work W required to lift an object varies...Ch. 3.5 - Prob. 71ECh. 3.5 - Prob. 72ECh. 3.5 - Music The fundamental frequency (in hertz) of a...Ch. 3.5 - Beam Load The maximum load that a horizontal beam...Ch. 3.5 - Prob. 75ECh. 3.5 - Prob. 76ECh. 3.5 - Prob. 77ECh. 3.5 - HOW DO YOU SEE IT? Discuss how well a linear model...Ch. 3.5 - Prob. 79ECh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Using Standard Form to Graph a Parabola In...Ch. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Geometry The perimeter of a rectangle is...Ch. 3 - Maximum Revenue The total revenue R earned (in...Ch. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Maximum Revenue A small theater has a seating...Ch. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Finding Real Zeros of a Polynomial Function In...Ch. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Using the Intermediate Value Theorem In Exercises...Ch. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Using the Intermediate Value Theorem In Exercises...Ch. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Using Synthetic Division In Exercises 57-60, use...Ch. 3 - Using Synthetic Division In Exercises 57-60, use...Ch. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Using the Rational Zero Test In Exercises 75-80,...Ch. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Using Descartes’s Rule of Signs In Exercises 93...Ch. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Measurement A billboard says that it is 12.5 miles...Ch. 3 - Energy The power P produced by a wind turbine is...Ch. 3 - Frictional Force The frictional force F between...Ch. 3 - Demand A company has found that the daily demand x...Ch. 3 - Prob. 105RECh. 3 - Cost The cost of constructing a wooden box with a...Ch. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Writing Explain the connections between factors of...Ch. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Write the standard form of the equation of the...Ch. 3 - The path of a ball is modeled by the function...Ch. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Divide using synthetic division. 2x43x2+4x1x+2Ch. 3 - Use synthetic division to show that x=3 is a zero...Ch. 3 - In Exercises 9 and 10, find the rational zeros of...Ch. 3 - Prob. 10TCh. 3 - In Exercises 11 and 12, find a polynomial function...Ch. 3 - Prob. 12TCh. 3 - In Exercises 13 and 14, find all the zeros of the...Ch. 3 - In Exercises 13 and 14, find all the zeros of the...Ch. 3 - In Exercises 15-17, find a mathematical model that...Ch. 3 - In Exercises 15-17, find a mathematical model that...Ch. 3 - In Exercises 15-17, find a mathematical model that...Ch. 3 - Prob. 18TCh. 3 - Prob. 1PSCh. 3 - Prob. 2PSCh. 3 - Building a Quonset Hut Quonset huts were developed...Ch. 3 - Prob. 4PSCh. 3 - Prob. 5PSCh. 3 - Prob. 6PSCh. 3 - Sums and Products of Zeros (a) Complete the table....Ch. 3 - Prob. 8PSCh. 3 - Finding the Equation of a Parabola The parabola...Ch. 3 - Prob. 10PSCh. 3 - Prob. 11PSCh. 3 - Prob. 12PSCh. 3 - Finding Dimensions At a glassware factory, molten...
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY