184 CHAPTER 3 Linear and Quadratic Functions Chapter Review Things to Know Linear function (pp. 139–145) f x mx b ( ) = + f m Average rate of change of = The graph of f is a line with slope m and y-intercept b. Quadratic function (pp. 157–166) f x ax bx c a , 0 2 ( ) = + + ≠ The graph of f is a parabola that is concave up if a 0 > and is concave down if a 0. < Vertex: b a f b a 2 , 2 ( ) ( ) − − Axis of symmetry: x b a2 = − y-intercept: f c 0( ) = x-intercept(s): If any, found by finding the real solutions of the equation ax bx c 0 2 + + = Objectives Section You should be able to . . . Examples Review Exercises 3.1 1 Graph linear functions (p. 139) 1 1(a)–3(a), 1(c)–3(c) 2 Use average rate of change to identify linear functions (p. 139) 2 1(b)–3(b), 4, 5 3 Determine whether a linear function is increasing, decreasing, or constant (p. 142) 3 1(d)–3(d) 4 Build linear models from verbal descriptions (p. 143) 4, 5 21 3.2 1 Draw and interpret scatter plots (p. 149) 1 29(a), 30(a) 2 Distinguish between linear and nonlinear relations (p. 150) 2, 3 29(b), 30(a) 3 Use a graphing utility to find the line of best fit (p. 152) 4 29(c) 3.3 1 Graph a quadratic function using transformations (p. 158) 1 6–8 2 Identify the vertex and axis of symmetry of a parabola (p. 160) 2 9–13 3 Graph a quadratic function using its vertex, axis, and intercepts (p. 161) 3–5 9–13 4 Find a quadratic function given its vertex and one other point (p. 164) 6 19, 20 5 Find the maximum or minimum value of a quadratic function (p. 164) 7–8 14–16, 22–27 3.4 1 Build quadratic models from verbal descriptions (p. 171) 1–3 22–28 2 Build quadratic models from data (p. 174) 4 30 3.5 1 Solve inequalities involving a quadratic function (p. 180) 1–3 17, 18 Review Exercises In Problems 1–3: (a) Find the slope and y-intercept of each linear function. (b) What is the average rate of change of each function? (c) Graph each function. Label the intercepts. (d) Determine whether the function is increasing, decreasing, or constant. 1. f x x2 5 ( ) = − 2. h x x 4 5 6 ( ) = − 3. G x 4 ( ) = In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, state its slope. 4. x y f x( ) = −1 −2 0 3 1 8 2 13 3 18 5. x y g x( ) = −1 −3 0 4 1 7 2 6 3 1
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