Chapter 2 Mid-Chapter Check Point

1 Mid- Chapter Check what values of is the function undefined? the equation of the vertical asymptote, or the vertical line that the graph of approaches but does the equation of the horizontal asymptote, or thehorizontal line that the graph of approaches but does ExercisesExercises 98 100 will help you prepare for the material covered inthe next section. Use the graph of function to solve each exercise. 112345 2 3 4 512345 1 2 3 4 5xyy = f(x)fMid- Chapter Check PointChapterWhat You Know:We performed operations with complex numbers and used the imaginary unit to represent solutions of quadraticequations with negative discriminants.

2 Only real solutionscorrespond to We graphed quadratic functionsusing vertices, intercepts, and additional points , as learned that the vertex of isand the vertex of is We used the vertex to solve problems thatinvolved minimizing or maximizing quadratic functions. Welearned a number of techniques for finding the zeros of apolynomial function of degree 3 or higher or, equivalently,finding the roots, or solutions, of the equation Forsome functions, the zeros were found by factoring Forother functions, we listed possible rational zeros and usedsynthetic division and the Factor Theorem to determine thezeros.

3 We saw that graphs cross the at zeros of oddmultiplicity and touch the and turn around at zeros ofeven multiplicity. We learned to graph polynomial functionsusing zeros, the Leading Coefficient Test, intercepts, andsymmetry. We checked graphs using the fact that apolynomial function of degree has a graph with at mostturning points . After finding zeros of polynomialfunctions, we reversed directions by using the LinearFactorization Theorem to find functions with given Exercises 1 6, perform the indicated operations and write theresult in standard and express solutions in standard form:In Exercises 8 11, graph the given quadratic function.

4 Give eachfunction s domain and +1f1x2=-x2-4x+5f1x2=5-1x+222f1x2=1x-322- 4x12x-32= +i1-i11+i214-3i23i12+ b2a, fA- +bx+c1h, k2f1x2=a1x-h22+ i2=-1Bi Ai=2-1,In Exercises 12 20, find all zeros of each polynomial graph the Exercises 21 26, solve each polynomial company manufactures and sells bath cabinets. The functionmodels the company s daily profit,when cabinets aremanufactured and sold per day. How many cabinets shouldbe manufactured and sold per day to maximize thecompany s profit? What is the maximum daily profit?

5 All pairs of numbers whose sum is find a pairwhose product is as large as possible. What is the maximumproduct? base of a triangle measures 40 inches minus twice themeasure of its height. For what measure of the height does thetriangle have a maximum area? What is the maximum area?In Exercises 30 31, divide, using synthetic division if Exercises 32 33, find an nth-degree polynomial function withreal coefficients satisfying the given and are zeros; (with multiplicity 2) and are zeros; have a real zero between 1 and 2?

6 F1x2=x3-x-5f102=363in=4;f1-12=8in=3;12x4 -13x3+17x2+18x-242,1x-4216x4-3x3-11x2+2x +42,13x2-12-18,xP1x2,P1x2=-x2+150x-44252 x4+x3-17x2-4x+6=0x4-x3-11x2=x+122x3+5x2- 200x-500=012x+1213x-22312x-72=06x3-11x2+ 6x-1=0x3-3x+2=0f1x2=-x3+5x2-5x-3f1x2=x3- 2x2+26xf1x2=2x3-2xf1x2=-6x3+7x2-1f1x2=-1 x+126f1x2=x4-5x2+4f1x2=x3-x2-4x+4f1x2=-1 x-2221x+122f1x2=1x-2221x+1232P-BLTZMC02_ 277-386-hr 19-11-2008 11:38 Page 339