Chapter 5: Exercises with Solutions

498 Chapter 5 Quadratic Functions22. f(x) = −x 2 − 8x − 823. f(x) = −x 2 − 8x − 924. f(x) = −x 2 + 10x − 2025. f(x) = 2x 2 − 20x + 4026. f(x) = 2x 2 − 16x + 1227. f(x) = −2x 2 + 16x + 828. f(x) = −2x 2 − 24x − 52In Exercises 29-32, perform each of thefollowing tasks for the given quadraticequation.i. Set up a coordinate system on a sheetof graph paper. Label and scale eachaxis. Remember to draw all lines witha ruler.ii. Show that the discriminant is negative.iii. Use the technique of completing thesquare to put the quadratic functionin vertex form. Plot the vertex onyour coordinate system and label itwith its coordinates. Draw the axis ofsymmetry on your coordinate systemand label it with its equation.iv. Plot the y-intercept and its mirrorimage across the axis of symmetryon your coordinate system and labeleach with their coordinates.v. Because the discriminant is negative(did you remember to show that?),there are no x-intercepts. Use thegiven equation to calculate one additionalpoint, then plot the point andits mirror image across the axis ofsymmetry and label each with theircoordinates.vi. Using all of the information on yourcoordinate system, draw the graph ofthe parabola, then label it with thevertex form of function. Use intervalnotation to describe the domain andrange of the quadratic function.29. f(x) = x 2 + 4x + 830. f(x) = x 2 − 4x + 931. f(x) = −x 2 + 6x − 1132. f(x) = −x 2 − 8x − 20In Exercises 33-36, perform each of thefollowing tasks for the given quadraticfunction.i. Set up a coordinate system on a sheetof graph paper. Label and scale eachaxis. Remember to draw all lines witha ruler.ii. Use the discriminant to help determinethe value of k so that the graphof the given quadratic function hasexactly one x-intercept.iii. Substitute this value of k back intothe given quadratic function, then usethe technique of completing the squareto put the quadratic function in vertexform. Plot the vertex on your coordinatesystem and label it with itscoordinates. Draw the axis of symmetryon your coordinate system andlabel it with its equation.iv. Plot the y-intercept and its mirrorimage across the axis of symmetryand label each with their coordinates.v. Use the equation to calculate an additionalpoint on either side of the axisof symmetry, then plot this point andits mirror image across the axis ofsymmetry and label each with theircoordinates.vi. Using all of the information on yourcoordinate system, draw the graphof the parabola, then label it withthe vertex form of the function. UseVersion: Fall 2007