Alg 1 Ch 9 Chapter Review pg 562

9.3 GRAPHING QUADRATIC FUNCTIONSExamples onpp. 518–520EXAMPLE To sketch the graph of y = x 2 º 4x º 3, first findb º 4the x-coordinate of the vertex: º = º = 2. Make a table of2 a 2 (1)values using x-values to the left and right of x = 2. Plot the pointsand connect them to form a parabola.x º1 0 1 2 3 4 5y 2 º3 º6 º7 º6 º3 211357yy x 2 4x 31 3 5 x(0, 3) (4, 3)(1, 6)(3, 6)(2, 7)Sketch the graph of the function. Label the vertex.11. y = x 2 º x º 5 12. y = ºx 2 º 3x + 2 13. y = º4x 2 + 6x + 39.4 SOLVING QUADRATIC EQUATIONS BY GRAPHINGExamples onpp. 526–528EXAMPLE To solve the quadratic equation ºx 2 + 3x = 2 bygraphing, first rewrite the equation in the form ax 2 + bx + c =0.º x 2 + 3x º 2 = 0.Sketch the graph of the related function y =ºx 2 +3x º 2. From the graph, the x-intercepts appear to be x = 1 and x =2.Check these in the original equation.yy x 2 3x 21 1 3 x1Solve the equation by graphing. Check the solution algebraically.14. x 2 + 2 = 3x 15. x 2 º 2x = 15 16. 1 2 x2 + 5x = º8 17. ºx 2 º 2x = º249.5 SOLVING QUADRATIC EQUATIONS BY THE QUADRATIC FORMULAExamples onpp. 533–5352(1)EXAMPLE Solve equations of the form ax 2 + bx + c = 0 by substituting thevalues of a, b, and c into the quadratic formula. Solve x 2 +6x º16=0.º6 ± 6 2 º4(1)(º16) º6 ± 36 + 64 º6 ± 100x = = = = º6 ±10 222 The equation has two solutions: x = º6 + 10 = 2 and x = º6 º 10 = º8.22Use the quadratic formula to solve the equation.18. 3x 2 º 4x + 1 = 0 19. º2x 2 + x + 6 = 0 20. 10x 2 º 11x + 3 = 0Chapter Review 563

9.6 APPLICATIONS OF THE DISCRIMINANTExamples onpp. 541–543EXAMPLES Use the discriminant, b 2 º4ac, to find the number of solutions of aquadratic equation ax 2 + bx + c =0.EQUATION DISCRIMINANT NUMBER OF SOLUTIONS3x 2 +6x +2=0 6 2 º 4(3)(2) = 12 22x 2 +8x +8=0 8 2 º 4(2)(8) = 0 1x 2 +7x +15=0 7 2 º 4(1)(15) = º11 0Tell if the equation has two solutions, one solution, or no real solution.21. 3x 2 º 12x + 12 = 0 22. 2x 2 + 10x + 6 = 0 23. ºx 2 + 3x º 5 = 09.7 GRAPHING QUADRATIC INEQUALITIESExamples onpp. 548–550EXAMPLE To sketch the graph of the quadratic inequalityy < x 2 º 9, first sketch the graph of the parabola y = x 2 º 9.Use a dashed parabola for inequalities with > or