Pre-Calculus 11 Workbook - McGraw-Hill Ryerson

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$Math and Chemistry - McGraw-Hill Ryerson$

The x-coordinate of the vertex is .The y-coordinate of the vertex is .How can you use the x-coordinate of the vertexto determine the y-coordinate of the vertex?The minimum value of the function is .The equation of the axis of symmetry isx = .What is the relationship between the x-coordinateof the vertex and the axis of symmetry?The factored form of the function is f(x) = x(x + 4), so the x-intercepts areand.The y-intercept is 0 because .The domain is {x| x ∈ R}.The range is {y | y ≥ –4, y ∈ R} because .b)y42-4 -2 0 2 4-2x-4The graph opens .The x-coordinate of the vertex is .The y-coordinate of the vertex is .The maximum value of the function is .The equation of the axis of symmetry is x = .The factored form of the function is f(x) =are and ., so the x-interceptsThe y-intercept is because .The domain is .The range is because .& After completing this example, you should be able to explain the solutions to Example 1on pages 167–168 of Pre-Calculus 11.14 MHR • Chapter 3 978-0-07-073882-9
Working Example 2: Using a Quadratic Function to Model a SituationA student council currently sells memberships for $6 per year and has 700 members. Toincrease revenue, they decide to increase the membership cost. The results of a survey indicatesthat 50 fewer students will buy a membership for every $1 increase in the membership cost.a) Write a quadratic function in standard form to model this situation.b) Graph the quadratic function. What does the shape of the graph communicate about thesituation?c) What are the coordinates of the vertex? What information does it give the student council?d) Determine if there are any x-intercepts that are relevant. What do these intercepts, if theyexist, represent in the situation?e) What domain and range are logical for this situation? Explain.Solutiona) Let x represent the number price increases and r(x) represent the revenue after a given priceincrease. Then,revenue = (price)(number of members)r(x) = (6 + x)(700 – 50x)The new price is $6 plus the number of priceincreases times $1, or 6 + 1x. The new numberr(x) = 4200 – 300x +of members is 700 minus the number of priceincreases times 50, or 700 – 50x.r(x) =b) Enter the function on a graphing calculator.Think about the maximumnumber of price increasespossible and revenueamounts to help youdetermine window settings.The shape of the quadratic confirms that if the council raises the membership price, revenueat first increases, but then decreases.c) The vertex of the graph is located at (4, 5000). This means that a price increase of ,to a new price of , will give the maximum revenue of $5000.978-0-07-073882-9 Pre-Calculus 11 Workbook • MHR 15
Page 2 and 3: Table of ContentsOverviewChapter 1
Page 5 and 6: Chapter 33.1 Investigating Quadrati
Page 7 and 8: Plot the vertex and these two other
Page 9 and 10: Check Your UnderstandingPractise1.
Page 11 and 12: ) y = -4(x + 7) 2 + 2y8642-5 05-2x-
Page 13 and 14: ) y = x 2 is transformed to y = 2(x
Page 16 and 17: 3.2 Investigating Quadratic Functio
Page 20 and 21: d) The x-intercept of indicates tha
Page 22 and 23: • Since the graph opens downward,
Page 24 and 25: c) a quadratic function with its ve
Page 26 and 27: 8. Sketch the graph of a quadratic
Page 28 and 29: c) What does the vertex represent i
Page 30 and 31: 3.3 Completing the SquareKEY IDEAS
Page 32 and 33: ) Method 1: Use AlgebraTo verify th
Page 34 and 35: Check Your UnderstandingPractise1.
Page 36 and 37: c) y = 1__2 (x - 5)2 - 4 and y = 1_
Page 38 and 39: 10. An animal rescue society needs
Page 40 and 41: ) Determine the quadratic function
Page 42 and 43: Chapter 3 Skills OrganizerComplete
Page 44: Chapter 3 Study CheckUse the chart

Pre-Calculus 11 Workbook - McGraw-Hill Ryerson

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