IB Pre-Calculus Chapter 2 Review Name: No Calculator Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. When an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. 1. The quadratic function f is defined by đ(đĨ) = 2đĨ 2 + 12đĨ + 11. (IBSL 2008 Paper 1) a). Express f in the form đ(đĨ) = 2(đĨ − â)2 + đ [3marks] b). Write down the vertex of the graph. [2 marks] c). Write down the equation of the axis of symmetry of the graph of f. [2 marks] d). Find the y-intercept of the graph of f. [2 marks] e). The x-intercepts of f can be written as pīą q , where đ, đ, đ ∈ ⤠. Find the values of đ, đ, đ. r [3 marks] d). Use your findings and graph the function f showing your vertex, x and y-intercepts. [2 marks] e). The graph of f is translated 4 units in the positive x-direction and 2 units in the positive y- direction. Find the function g for the translated graph, giving your answer in the form đ(đĨ) = 2(đĨ − đ)2 + đ. [4 marks] 2. Let đ(đĨ) = đ(đĨ − 4)2 + 3 a. Write down the coordinates of the vertex of the curve of f. [2 marks] b. Given that đ(2) = 12, find the value of a. [2 marks] c. Find the y-intercept of the curve of f. [2 marks] 3. Find the zeros of the polynomial function and state the multiplicity of each. đ(đĨ) = −9đĨ 3 (đĨ − 5)2 (đĨ + 4)5 [9 marks] 4. Solve the equation: 5. Find the equation of the line for which đ(3) = 5 and đ(8) = 2 6. Find the vertex and axis of symmetry of the quadratic đ(đĨ) = 3đĨ 2 − 12đĨ + 3. [4 marks] 3 đĨ+2 + 6 đĨ 2 +2đĨ = 3−đĨ đĨ [10 marks] [4 marks] 7. Find the quadratic that contains the point (6, −5) and vertex (4, 3). [4 marks] 8. Find the zeros of the polynomial đ(đĨ) = 3đĨ 3 + 2đĨ 2 − 1đĨ. [6 marks] 9. Divide the polynomial đ(đĨ) = 4đĨ 3 + 9đĨ 2 − 3đĨ − 10 by đ(đĨ) = đĨ + 4 and write a summary statement in fraction form. [6 marks] 10. Sketch the general shape of the graph of the polynomial đ(đĨ) = đĨ(đĨ − 3)2 (đĨ + 5)3 . [6 marks] 11. Determine whether (đĨ − 3) is a factor of đ(đĨ) = 4đĨ 4 − 6đĨ 3 − 7đĨ 2 − 9. Show how you arrived at your answer. [5 marks] 12. Write down the equation that will help you find the least perimeter for a rectangle with an area of 400 square meters. [8 marks]