Chapter 5: Exercises with Solutions

474 Chapter 5 Quadratic FunctionsIn Exercises 23-30, perform each of thefollowing tasks for the given quadraticfunction.i. Set up a coordinate system on graphpaper. Label and scale each axis. Rememberto draw all lines with a ruler.ii. Use the technique of completing thesquare to place the quadratic functionin vertex form. Plot the vertexon your coordinate system and labelit with its coordinates. Draw the axisof symmetry on your coordinate systemand label it with its equation.iii. Use a strictly algebraic technique (nocalculators) to find the x-interceptsof the graph of the given quadraticfunction. Plot them on your coordinatesystem and label them withtheir coordinates.iv. Find the y-intercept of the graph ofthe quadratic function. Plot the y-intercept on your coordinate systemand its mirror image across the axisof symmetry, then label these pointswith their coordinates.v. Using all the information plotted, drawthe graph of the quadratic functionand label it with the vertex form ofits equation. Use interval notation todescribe the domain and range of thequadratic function.23. f(x) = x 2 + 2x − 824. f(x) = x 2 − 6x + 825. f(x) = x 2 + 4x − 1226. f(x) = x 2 + 8x + 1230. f(x) = −x 2 − 8x + 20In Exercises 31-38, factor the given quadraticpolynomial.31. 42x 2 + 5x − 232. 3x 2 + 7x − 2033. 5x 2 − 19x + 1234. 54x 2 − 3x − 135. −4x 2 + 9x − 536. 3x 2 − 5x − 1237. 2x 2 − 3x − 3538. −6x 2 + 25x + 9In Exercises 39-46, find the zeros ofthe given quadratic functions.39. f(x) = 2x 2 − 3x − 2040. f(x) = 2x 2 − 7x − 3041. f(x) = −2x 2 + x + 2842. f(x) = −2x 2 + 15x − 2243. f(x) = 3x 2 − 20x + 1244. f(x) = 4x 2 + 11x − 2045. f(x) = −4x 2 + 4x + 1546. f(x) = −6x 2 − x + 1227. f(x) = −x 2 − 2x + 828. f(x) = −x 2 − 2x + 2429. f(x) = −x 2 − 8x + 48Version: Fall 2007