Pre-Calculus 11 Workbook - McGraw-Hill Ryerson

More documents

Recommendations

Info

$Math and Chemistry - McGraw-Hill Ryerson$

Working Example 1: Sketch the Graph of a Quadratic in Vertex FormState the vertex, the direction of opening, the equation of the axis of symmetry, the domainand range, and the maximum or minimum value of the graph of y = –3(x + 4) 2 + 1. Then,sketch the graph. SolutionUse the values of a, p, and q to determine some characteristics of the function and sketch thegraph.y = –3(x + 4) 2 + 1Which of the parameters a, p, and qa p qdetermine the coordinates of the vertex?The vertex is ( , ).Since a < 0, the graph opensThe equation of the axis of symmetry is .The domain of the quadratic is {x | x ∈ R}.The range is {y | y ≤ , y ∈ R }.(upward or downward).The (maximum or minimum) value is .Determine the coordinates of a point (other than the vertex) on the graph.Choose an x-coordinate and determine the corresponding y-coordinate.Choose x = –3. Substitute this value of x into the function to determine y.y = –3(x + 4) 2 + 1y = –3(–3 + 4) 2 + 1y = –3(1) 2 + 1y = –2So, one point on the graph is ( , ).Since every parabola is symmetric about its axis of symmetry, this means that another point onthe graph is ( , –2).Which of the parameters a, p, and qdetermine the equation of the axisof symmetry?How can you use the value of q tohelp you determine the range?2 MHR • Chapter 3 978-0-07-073882-9
Plot the vertex and these two other points to sketch the graph.y8642-5 05-2x-4-6-8& Compare this method with the two methods shown on pages 148–149 of Pre-Calculus 11.Working Example 2: Determine a Quadratic Function in Vertex FormGiven Its GraphDetermine a quadratic function, in vertex form, for the graph.y8642-5 05-2x-4-6-8SolutionThe vertex of the graph is . So, p = and q = .Then, the equation of the function in the form y = a(x – p) 2 + q is .Substitute the coordinates of any point from the graph, except the vertex, into the function todetermine the value of a.978-0-07-073882-9 Pre-Calculus 11 Workbook • MHR 3
Page 2 and 3: Table of ContentsOverviewChapter 1
Page 5: Chapter 33.1 Investigating Quadrati
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 18 and 19: The x-coordinate of the vertex is .
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?