IB Math Analysis & Approaches SL Chapter 3: Linear and Quadratic Functions PDF
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This document is a set of notes for an IB Math Analysis and Approaches SL course on Quadratic Functions. It covers graph sketching, various forms of quadratic functions (vertex, general, and factored forms), and exercises. The notes include definitions and practical examples for the use of these functions.
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Chapter 3: Linear and Quadratic Functions 3.4 Graphing quadratic functions Essential Questions: How can we change from the general to vertex to factored form of a quadratic function? How are each of these forms used to identify key features of the graph? Quadratic Functions y...
Chapter 3: Linear and Quadratic Functions 3.4 Graphing quadratic functions Essential Questions: How can we change from the general to vertex to factored form of a quadratic function? How are each of these forms used to identify key features of the graph? Quadratic Functions y Sketch the graph of the quadratic function and 12 label all key points: 9 6 f (x) = −0.5x 2 + 7.5x − 18 3 Domain: −6 −3 0 3 6 9 12 15 x −3 Range: −6 x-intercepts: −9 y -intercepts: −12 Vertex: −15 −18 IB Math Analysis & Approaches SL 1/12 Vertex Form Vertex Form The vertex form of a quadratic function is written as follows: f (x) = a(x − h)2 + k, where a, h, k ∈ R and a 6= 0. 1. Why can a not equal zero? 2. What is the significance of h and k? 3. What is the equation of the axis of symmetry? 4. How do we determine whether the parabola is concave up or concave down? IB Math Analysis & Approaches SL 2/12 General Form General Form The general form of a quadratic function is written as follows: f (x) = ax 2 + bx + c, where a, b, c ∈ R and a 6= 0. b 1. What is the significance of − 2a ? 2. What are the coordinates of the vertex? 3. What is the y -intercept? IB Math Analysis & Approaches SL 3/12 Factorized Form Factorized Form The factorized form of a quadratic function is written as follows: f (x) = a(x − p)(x − q), where a, p, q ∈ R and a 6= 0. 1. What is the significance of p and q? 2. What is the equation of the axis of symmetry? 3. What are the coordinates of the vertex? IB Math Analysis & Approaches SL 4/12 Quadratic Functions Sketch the graph of each function and label the key features of the graph: 1. f (x) = 2(x + 3)2 − 6 2. f (x) = −x 2 + 6x − 4 3. f (x) = (x − 4)(x − 2) IB Math Analysis & Approaches SL 5/12 Textbook Exercises Textbook Exercises To practice and apply these concepts, work through the following exercises: Exercise 3L p.143 #1-6 Exercise 3M p.149 #1-4 IB Math Analysis & Approaches SL 6/12 Quadratic Functions Write the equation of the quadratic function f (x) = −4x 2 + 2x in factorized form. Write down the coordinates of the x- and y -intercepts and the vertex. IB Math Analysis & Approaches SL 7/12 Quadratic Functions Write the equation of the quadratic function f (x) = 3(x − 1)(x + 2) in general form. Write down the coordinates of the x- and y -intercepts and the vertex. IB Math Analysis & Approaches SL 8/12 Quadratic Functions Write the equation of the quadratic function f (x) = − 12 (x − 4)2 − 2 in general form. Write down the coordinates of the y -intercept and the vertex. IB Math Analysis & Approaches SL 9/12 Quadratic Functions Write the equation of the quadratic function in all three forms. y 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 x −1 −2 −3 IB Math Analysis & Approaches SL 10/12 Textbook Exercises Textbook Exercises To practice and apply these concepts, work through the following exercises: Exercise 3N p.151 #1-6 Exercise 3O p.153 #1-3 IB Math Analysis & Approaches SL 11/12 Assignment: 1. Process your notes Chunk the information by numbering each big idea Circle key words and new vocabulary Highlight main ideas Fill in any gaps and add clarifying comments Write questions next to any points of confusion 2. Textbook Exercises: Read pp.142-154 3L p.151 #3 3M p.149 #1c, 2c, 3c, 4c 3N p.151 #1b, 2b, 3b, 6 3O p.153 #3 IB Math Analysis & Approaches SL 12/12
