Pre-Calc/Chapter 2: Polynomial, Power, and Rational Functions/2.3 Polynomial Functions with Modeling/2.3.1 Describe End BehaviorDescribe the end behavior of the polynomial function by finding f and f = (x...Describe the end behavior of the polynomial function by finding f and
f = (x - 3) ( 1 - x) (3x - 5)]]>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∞Incorrect∞, -∞Incorrect-∞, ∞Correct-∞, -∞IncorrectDescribe the end behavior of the polynomial function by finding f and f = -x3...Describe the end behavior of the polynomial function by finding f and
f = -x3 + 4x2 - 4x - 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-∞Incorrect∞, ∞Incorrect∞, -∞Incorrect-∞, ∞CorrectDescribe the end behavior of the polynomial function by finding f and f = x3 ...Describe the end behavior of the polynomial function by finding f and
f = x3 - x4 + 2x2 + 3x - 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∞Incorrect-∞, -∞Correct∞, ∞Incorrect∞, -∞IncorrectPre-Calc/Chapter 2: Polynomial, Power, and Rational Functions/2.3 Polynomial Functions with Modeling/2.3.2 Find Zeros Find cubic function from zerosFind a cubic function in standard form with the given zeros.
#a , #b , #c
Express answer in this format: f(x) = ax2 + bx + c
]]>1.00000000.333333300f(x)=#answer]]>Great job!]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Find real zeros by factoringFind the zeros of the function.
]]>1.00000000.33333330truetrueABCDYour answer is correct.]]>Your answer is partially correct.]]>Your answer is incorrect.]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo»,«/mo»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«/math»]]>Correct!]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«mo»,«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«/math»]]>Incorrect]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«/math»]]>Incorrect.]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math»]]>Incorrect]]>Answer not shown]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>25</mn><mo>,</mo><mn>36</mn><mo>,</mo><mn>49</mn><mo>,</mo><mn>64</mn><mo>,</mo><mn>81</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mi>a</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Find the zeros of the polynomial function and state the multiplicity of each....Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = -6x2(x - 8)(x + 1)3]]>1.00000000.33333330truetrueabc-1, multiplicity 3; 0, multiplicity 2; 8, multiplicity 1Correct-1, multiplicity 3; 0, multiplicity 2; 1, multiplicity 1; 8, multiplicity 1Incorrect-1, multiplicity 1; 1, multiplicity 1; 8, multiplicity 1Incorrect-1, multiplicity 3; 8, multiplicity 1IncorrectMatch the given graph with its polynomial function.Match the given graph with its polynomial function.
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+ x3 - 12x2 + 10]]>Incorrect5 - 4x3 + 12x2 + 10]]>Incorrect5 - 10x2 - 10]]>Incorrect4 + x3 - 10x2 + 10]]>CorrectUse a graphing calculator to approximate the real zeros of the function ...Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth.
f(x) = 5x4 + 10x3 + 5x2 - 5x + 1]]>1.00000000.33333330truetrueabc-5.08, 0.16Incorrect-2.54, -0.16IncorrectNo real solutionCorrect0.16IncorrectUse a graphing calculator to approximate the real zeros of the function ...Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth.
f(x) = 5x4 + 10x3 - 5x2 +5x + 1]]>1.00000000.33333330truetrueabc-5.08, 0.16Incorrect-2.54, -0.16Correct0.16IncorrectNo real solutionIncorrectPre-Calc/Chapter 2: Polynomial, Power, and Rational Functions/2.3 Polynomial Functions with Modeling/2.3.3 Solve ApplicationsSolve the problem.A piece of rectangular sheet metal is 25 inches wide. It is...Solve the problem.
A piece of rectangular sheet metal is 25 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of x will the area of the cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary, round to 2 decimal places.]]>1.00000000.33333330truetrueabc100Incorrect50Incorrect6.25Correct12.5IncorrectSolve the problem.A rectangular piece of cardboard measuring 15 inches by 42 ...Solve the problem.
A rectangular piece of cardboard measuring 15 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.]]>1.00000000.33333330truetrueabc31.29Incorrect3.36Correct15.64Incorrect18.03IncorrectSolve the problem.A rectangular piece of cardboard measuring 30 inches by 43 ...Solve the problem.
A rectangular piece of cardboard measuring 30 inches by 43 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.]]>1.00000000.33333330truetrueabc889.17Incorrect50,922.98Incorrect3351.01Correct777.08IncorrectSolve the problem.The polynomial function I(t) = -.1t2 + 1.5t represents the ...Solve the problem.
The polynomial function I(t) = -.1t2 + 1.5t represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline? Round to the nearest tenth of a year, if necessary.]]>1.00000000.33333330truetrueabc7.5 yearsCorrect6.5 yearsIncorrect15 yearsIncorrect10 yearsIncorrectSolve the problem.The polynomial function L(p) = p3 - 5p2 + 20 gives the rate...Solve the problem.
The polynomial function L(p) = p3 - 5p2 + 20 gives the rate of gas leakage from a tank as pressure increases in p units from its initial setting. Will an increase of 2 units result in a lower rate of leakage compared to the initial setting?]]>1.00000000.33333330truetrueabcYesCorrectNoIncorrectUse a cubic or quartic regression (as specified) to fit a curve through the ...Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth.
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and 
= (x - 3) ( 1 - x) (3x - 5)]]>
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and 
= -x3 + 4x2 - 4x - 6]]>
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and 
= x3 - x4 + 2x2 + 3x - 1]]>
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(Quartic)]]>