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142 CHAPTER 3 Linear and Quadratic Functions

3.3 Assess Your Understand]'Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

1. List the intercepts of the equation y = x2 - 9. (pp, 11-12) 3. To complete the square of X2 - 5x, you add the number2. Find the real solutions of the equation 2x2 + 7x - 4 = 0. __ . (pp. A47-A4~)(pp, A4~-;\) 1) 4. To graph y = (x - 4)2, you shift the graph of y = x2 to the

__ a distance of __ units. (pp.Y2-IOO)Concepts and Vocabulary5. The graph of a quadratic function is called a(n) __ .6. The vertical line passing through the vertex of a parabola is

called the7. The x-coordinate of the vertex of f(x) =ax' + bx + c,

a v: O,is __ .8. True or False The graph of f (x) = 2x2 + 3x - 4 opens up.

9. True or False The y-coordinate of the vertex of f(x) =-x2 + 4x + 5 is f(2).

10. True or False If the discriminant b2 - 4ac =0, the graph off(x) =ax: + bx + c, a -:/-0, will touch the x-axis at itsvertex.

Skill Building

2 x -2 2 x-2 ! 2 x I -2 (0,-1) -2 2 x-1 -2 -1(-1,0) (-1, -1)

E y F y G y H y1 2

-2-2 x-1 (1,0) 3 x -1 3 x (1,-1)

-2 -1 -2

In Problems 19-34, graph the function f by starting with the graph of y =x2 and using transformations (shifting, compressing, stretching,and/or reflection).[Hint: H necessary, write fin the formf(x) =a(x - h)2 + k .]119. f(x) ="4X2

123. f(x) ="4x2 + 227. f(x) =x2 + 4x + 2

In Problems 11-18, match each graph to one the following functions.11. f (x) = x2 - 1 12. f (x) = - X2 - 1 13. f (x) = x2 - 2x + 115. f(x) = x2 - 2x + 2 16. f(x) = x2 + 2x 17. f(x) = x2 - 2xA y Bye y

322

20. f(x) =2x2 121. f (x) = 4 X2 - 2125. f(x) ="4x2 + 1

29. f(x) =2x2 - 4x + 1133. f (x) =2 x2 + x-I

24. f(x) = 2x2 + 428. f(x) = x2 - 6x - 1

31. f(x) =-x2 - 2x 32. f(x) = _2x2 + 6x + 2

14. f(x) = x2 + 2x + 118. f (x) =x2 + 2x + 2D y

3(-1,1)

22. f(x) = 2X2 - 326. f(x) =-2x2 - 230. f(x) = 3x2 + 6x

2 2 434 f(x)=-x +-x-l33In Problems 35-52, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axisof symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where thefunction is increasing and where it is decreasing.J5. f(x) = X2 + 2x 36. f(x) = x2 - 4x38. f(x) = -x2 + 4x 39. f(x) = 2x2 - 8x41. f(x) =x2 + 2x - 8 42. f(x) =x2 - 2x - 344. f (x) = X2 + 6x + 9 45. f (x) = 2X2 - X + 2

37. f(x) = -x2 - 6x40. f(x) =3x2 + 18x43. f(x) =X2 + 2x + 146. f(x) =4x2 - 2x + 1

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