141. This question assesses the student’s ability to find solutions to graph quadratic functions and describe characteristics of the function. (a) There is a when 0; . The is at (0, 1). y-intercept x= y-intercept The occur when = 0; . x-intercepts y Since the at and or approximately (0.37, 0) and (–1.37, 0). x-intercepts (b) The axis of symmetry is at (c) The of the vertex is at . The is . The vertex is at . x-coordinate y-coordinate (d) (e) The domain is all real numbers, the range is . 148. . This question assesses the student’s ability to derive the equation of a quadratic from a graph, find its zeros, and compute the rate of change between two points. (a) The vertex of the quadratic is at (1, 5), so the equation is of the form . The at (0, 4) is a solution, so . y-intercept Thus, the equation of the parabola is . (b) Its are where . x-intercepts (c) The average rate of change of the function between (0, 4) and (1, 5) is . 149. This question assesses the student’s ability to define and sketch quadratic functions with certain characteristics. Answers will vary. (a) should be of the form, or equivalent to, where > 0 and > 0. f a k (b) should be of the form, or equivalent to, where < 0. g a (c) should be of the form, or equivalent to, where . h 156. This question assesses the student’s ability to factor, solve, and graph a quadratic function; and solve a system of a quadratic and a linear function. (a) (b) (c) The key points are the at (–4, 0) and (2, 0), the at (0, and the vertex at (–1, x-intercepts y-intercept –16), –18).
141. This question assesses the student’s ability to find solutions to graph quadratic functions and describe characteristics of the function. (a) There is a y-intercept when x= 0; . The y-intercept is at (0, 1). The x-intercepts occur when y = 0; . Since the x-intercepts at and or approximately (0.37, 0) and (–1.37, 0). (b) The axis of symmetry is at (c) The x-coordinate of the vertex is at . The y-coordinate is . The vertex is at . (d) (e) The domain is all real numbers, the range is . 148. . This question assesses the student’s ability to derive the equation of a quadratic from a graph, find its zeros, and compute the rate of change between two points. (a) The vertex of the quadratic is at (1, 5), so the equation is of the form . The y-intercept at (0, 4) is a solution, so . Thus, the equation of the parabola is . (b) Its x-intercepts are where . (c) The average rate of change of the function between (0, 4) and (1, 5) is . 149. This question assesses the student’s ability to define and sketch quadratic functions with certain characteristics. Answers will vary. (a) f should be of the form, or equivalent to, where a > 0 and k > 0. (b) g should be of the form, or equivalent to, where a < 0. (c) h should be of the form, or equivalent to, where . 156. This question assesses the student’s ability to factor, solve, and graph a quadratic function; and solve a system of a quadratic and a linear function. (a) (b) (c) The key points are the x-intercepts at (–4, 0) and (2, 0), the y-intercept at (0, –16), and the vertex at (–1, –18).