Pre-Calc/Chapter 2: Polynomial, Power, and Rational Functions/2.1 Linear//Quadratic Functions and Modeling/2.1.2 Quadratic Functions Complete the square Complete the square to get the proper values for Vertex Form     y= a (x - h)2+ k
y = x2 - #p x + 18

]]> 1.0000000 0.3333333 0 0 a=#ah=#hk=#k]]> Nice 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>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>14</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>(</mo><mfrac><mi>p</mi><mn>2</mn></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>18</mn><mo>-</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mn>4</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>h</mi><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>k</mi><mo>=</mo><mo>#</mo><mi>k</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">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">20 40 40</data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Find degree of polynomial If the following is a polynomial function, then state its degree. If it is not, then enter 0.

«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»«mo»§#160;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#160;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«/msup»«mo»-«/mo»«mn»12«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <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>5</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>2</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><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>(</mo><mo>)</mo><mo>=</mo><msup><mi>ax</mi><mi>b</mi></msup><mo>+</mo><msup><mi>cx</mi><mi>d</mi></msup><mo>+</mo><msup><mi>ex</mi><mi>f</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>p</mi><mo>(</mo><mo>)</mo></mrow><mrow><mi>d</mi><mo>&gt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>d</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><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 the axis of symmetry of the graph of the function.f(x) = 3x2 + 30x + 78 Find the axis of symmetry of the graph of the function.

f(x) = 3x2 + 30x + 78

]]> 1.0000000 0.3333333 0 true true abc x = 3

]]> Incorrect

]]> x = 6

]]> Incorrect

]]> x = -2

]]> Incorrect

]]> x = -5

]]> Correct

]]> Find the axis of the graph of the function.f(x) = (x + 3)2 + 4 Find the axis of the graph of the function.

f(x) = (x + 3)2 + 4]]> 1.0000000 0.3333333 0 true true abc y = -3 Incorrect x = -3 Correct x = 3 Incorrect x = 0 Incorrect Find the axis of the graph of the function.f(x) = 2x2 + 20x + 51 Find the axis of the graph of the function.

f(x) = 2x2 + 20x + 51]]> 1.0000000 0.3333333 0 true true abc x = 1 Incorrect x = 6 Incorrect x = -5 Correct x = 0 Incorrect Find the axis of the graph of the function.f(x) = 3x2 + 6x + 8 Find the axis of the graph of the function.

f(x) = 3x2 + 6x + 8]]> 1.0000000 0.3333333 0 true true abc x = 5 Incorrect x = -4 Incorrect x = 2 Incorrect x = -1 Correct Find the vertex of the graph of the function.f(x) = -4x2 - 16x - 22 Find the vertex of the graph of the function.

f(x) = -4x2 - 16x - 22]]> 1.0000000 0.3333333 0 true true abc (3, 7) Incorrect (7, 3) Incorrect (-6, -2) Incorrect (-2, -6) Correct Find the vertex of the graph of the function.f(x) = (x - 2)2 + 3 Find the vertex of the graph of the function.

f(x) = (x - 2)2 + 3

]]> 1.0000000 0.3333333 0 true true abc (0, 2)

]]> Incorrect

]]> (3, 0)

]]> Incorrect

]]> (3, 2)

]]> Incorrect

]]> (2, 3)

]]> Correct

]]> (-2,-3)

]]> Find the vertex of the graph of the function.f(x) = (x + 5)2 + 1 Find the vertex of the graph of the function.

f(x) = (x + 5)2 + 1]]> 1.0000000 0.3333333 0 true true abc (1, -5) Incorrect (1, 0) Incorrect (-5, 1) Correct (0, -5) Incorrect Find the vertex of the graph of the function.f(x) = 2(x - )2 + 2 Find the vertex of the graph of the function.

f(x) = 2(x - )2 + 2]]> 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 1.0000000 0.3333333 0 true true abc , 2)]]> 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 Incorrect (-6, 2) Incorrect (6, 2) Incorrect , 2)]]> 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 Correct Find the vertex of the graph of the function.f(x) = 3(x - 1)2 + 6 Find the vertex of the graph of the function.

f(x) = 3(x - 1)2 + 6]]> 1.0000000 0.3333333 0 true true abc (1, 6) Correct (1, -6) Incorrect (-1, 6) Incorrect (-1, -6) Incorrect Find the vertex of the graph of the function.f(x) = 3x2 + 18x + 29 Find the vertex of the graph of the function.

f(x) = 3x2 + 18x + 29]]> 1.0000000 0.3333333 0 true true abc (-3, 2) Correct (-1, 4) Incorrect (2, -3) Incorrect (4, -1) Incorrect Maximum height of projectile A projectile is thrown upward so that its distance above the ground after t seconds is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mn»16«/mn»«msup»«mi»t«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»t«/mi»«/math».  After how many seconds does it reach its maximum height?  Round to tenths.

]]> 1.0000000 0.3333333 0 0 #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>250</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>a</mi></mrow><mrow><mo>-</mo><mn>32</mn></mrow></mfrac><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">2</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> Solve the problem.  A projectile is thrown upward so that its distance ... Solve the problem.  

A projectile is thrown upward so that its distance above the ground after t seconds is  After how many seconds does it reach its maximum height?]]> /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAAUAF8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9MvBHj3RfiLpM+paFPcT2sF3NYzC6sp7SWOeJykiNHMiOCGBHK4PbIroa+NbCz1G2i1rx7pqfEq11C1+I8bNpgsdXtoG0qW+QTuumrGq3SNC8jmRopXXsy7FVfbfjj4c+Kuu32lN8Otc/si2jjkF4v9s2ljvckbTifRtQLYGeQ0ePRuozpycqcJtau1/XlTfy1t6jkkqk4LZN/wDpTX6X/E9drN8ReItO8KaNdarq10tnYWyhpJWBY5JAVVUAszMxCqqgszEAAkgVyHgHRviDYfDN7LX9atH8anzfL1G+kTVYEJb92XFva6cJFA/hWOM9t561Los3jPwfpOsan471/SPEdpBD5kUXhTwpe29wmM7v3Qu7uScnjCxqDwfvZ4t6J62sgjZtXRq6T8S/DGs/D608cwaxBF4TubJdQj1S7DW0Yt2G4OwlCsnB6MAfaobTx1b+LdFb/hHJxaa3c28stnZ+IrG5sJgEcRtM9rMkc5jVmXnaobKgMNwavlbSNP1++/Zq+AkYt/GXhuy8MXluniFLTwpczapZyRWcqRSR2U0DPMEneIh1gmQEB9p8sstnRvCPjXxB8V9C1vUNY8ZWWv3mi6pYeHvE+paRqBtlUXcbW0upWFrJBbQyNBuPlzpCrssbPGsiCMazilUcEtNbeii2te7sktu68iTUdYu9mv8A0qz+SWreva3f6H+FXibxhf674v8AD/i9tI1K50O4t0h1rQrOWztrlZYFkMTQSTTNHLHkFh5rArLE3y7iK9Grz34QeBvFfgHTJtO8Qa94f1q0GHhbR9CuLCYykkyyzyTX1yZnckEt8pzkknPHNaP4Y+MEP7Q2qatf+J9Fm+Hj6XbRxWcekTruYT3RaNAdQYJOFaEvcGIrIuxQilCaLKTevQVkk2un+f8AX/DHo3jLx9ongGzt59YuJ1e5cxW1nY2c17d3TgFmWG3gR5ZSqgsQiHaqljgAmuR139pDwR4c1a60+/PiRGtbiO1uLuLwlq01lFK+zarXSWphH+sQHL/KTg4INeS/Gyz8ZaT8b9f1vTdX8Y6RPc+Gray8MSeGPDCavDPdrJO8tvcyPBNHbo8jWxYubYOAp88CI7fWBqWq+JfFkY17R7q00jwnYxahetHZyyR3+pvFuC2yhS06QLuPyBsySRhfniYVley5n/X9L06LzY072X9bfq/PRN+m14M+M/hPx5qWp6dpl7eW+oadAl3cWusaVd6ZL9nYsqzot1FGZISUceam5MjrXX2F/a6rY217ZXMN5ZXMazQXNu4eOWNgCrqw4ZSCCCOCDXzxpPiLT/jbN4xvbnRPGGka9e6Bc6bp1pc+HNZ0Z7S0yWK/bZIIVNxK/lsVjk+UIqpu2u79Z+y1c6Xpfwk8KeGrG08W2t1YaNbSXKeKdO1SGRJNvlugkvV4w8b4iRyEXaVARkJpK6d91b535vysr9m7a7ineM0ltr+HL+bbt3Suex0UUUhhRRRQAUUUUAFFFFABRRRQAUUUUAf/2Q== 1.0000000 0.3333333 0 true true abc 31.5 s Incorrect 42 s Incorrect 10 s Incorrect 21 s Correct Solve the problem.  The number of mosquitoes M(x), in millions, in a ... Solve the problem.  

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 20x - x2. What rainfall produces the maximum number of mosquitoes?]]> 1.0000000 0.3333333 0 true true abc 0 in. Incorrect 10 in. Correct 20 in. Incorrect 400 in. Incorrect Solve the problem.  The perimeter of a rectangle is 82 m. If the width were... Solve the problem.  

The perimeter of a rectangle is 82 m. If the width were doubled and the length were increased by 18 m, the perimeter would be 150 m. What are the length and width of the rectangle?]]> 1.0000000 0.3333333 0 true true abc width 25 m, length 16 m Incorrect width 20 m, length 20 m Incorrect width 15 m, length 20 m Incorrect width 16 m, length 25 m Correct Solve the problem.  The stadium vending company finds that sales of hot ... Solve the problem.  

The stadium vending company finds that sales of hot dogs average 40,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price per hot dog should the vending company charge to realize the maximum revenue?]]> 1.0000000 0.3333333 0 true true abc $3.50 Incorrect $4.00 Incorrect $3.25 Correct $1.50 Incorrect Solve the problem.

The profit made when t units are sold, t > 0, is given by  Determine the number of units to be sold in order for P > 0 (a profit is made).

]]> 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 1.0000000 0.3333333 0 true true ABCD 19 < t < 14

]]> Incorrect

]]> t = 19 or t = 14

]]> Incorrect

]]> t = 33

]]> Incorrect

]]> t > 19 or t < 14

]]> Correct

]]> Answer not shown

]]> Write an equation for the quadratic function whose graph contains the given ... Write an equation for the quadratic function whose graph contains the given vertex and point.

Vertex (5, 5), point (7, 17)]]> 1.0000000 0.3333333 0 true true abc 2 - 5x + 5]]> Incorrect 2 - 30x + 5]]> Incorrect 2 - 30x + 80]]> Incorrect 2 - 30x + 80]]> Correct Write an equation for the quadratic function whose graph contains the given ... Write an equation for the quadratic function whose graph contains the given vertex and point.

Vertex (5, 5), point (7, 17)

]]> 1.0000000 0.3333333 0 true true ABCD P(x) = -3x2 - 30x + 5

]]> Incorrect

]]> P(x) = 7x2 - 30x + 80

]]> Incorrect

]]> P(x) = 3x2 - 5x + 5

]]> Incorrect

]]> P(x) = 3x2 - 30x + 80

]]> Correct

]]> P(x) = -3x2 + 5x - 30

]]> Write an equation for the quadratic function whose graph contains the given ... Write an equation for the quadratic function whose graph contains the given vertex and point.

Vertex (3, -2), point (-4, 145)]]> 1.0000000 0.3333333 0 true true abc 2 + 18x - 2]]> Incorrect 2 - 18x + 25]]> Correct 2 - 18x - 25]]> Incorrect 2 - 3x - 2]]> Incorrect Write the quadratic function in vertex form.y = x2 - 10x + 18 Write the quadratic function in vertex form.

y = x2 - 10x + 18]]> 1.0000000 0.3333333 0 true true abc 2 - 7]]> Incorrect 2 - 7]]> Correct 2 + 7]]> Incorrect 2 + 7]]> Incorrect Write the quadratic function in vertex form.y = x2 + 4x Write the quadratic function in vertex form.

y = x2 + 4x]]> 1.0000000 0.3333333 0 true true abc 2 - 16]]> Incorrect 2 + 4]]> Incorrect 2 + 2]]> Incorrect 2 - 4]]> Correct