- f(x) = x2, f(x) = - 3 x 2, f(x) = 5x2
- f(x) = -§ x 2, f(x) = —2x2, f(x) = —4x2
-\- -i
20
/
\ -tr
V
-8
/ .........
4 -19
■«
\/T
(-4 f
(^0) / X
-4
■V /
- a
about 2.2 s
- domain: all real numbers; range: f(x) > 6
31. domain: all real numbers; range: y < - 9
33. Answers will vary. Sample: If a > 0, the parabola
opens upward. If a < 0, the parabola opens downward.
The vertex of the parabola is (0, c). 35. A
37a. g(x) = 3x2 + 6 ; the graph of g(x) is shifted up
4 units and is narrower than the graph of f(x).
.(2 ,
domain: all real numbers;
range: f(x) > 0
domain: all real numbers;
range: y < 0
Exercises 7 3); m a xim u m 9. (2, 0); m in im u m
domain: all real numbers;
range: f(x) a 0
b. h(x) = 9x 2 + 2; the graph of h(x) is narrower than the
graph of f(x). c. Multiplying a quadratic function by a
number shifts the graph up or down and changes the
width of the parabola. Multiplying the x value of a
quadratic function by a number only changes the width of
the parabola.
41.
1
Ww m i i i i r i | T
vertex: (0, 3) vertex: (0, - 6 )
axis of symmetry: x = 0 axis of symmetry: x = 0
- M 45. M 47a. a > 0 b. |a| > 1 49a. graph of a
parabola in the first quadrant, pointing down, with
intercepts (0, 135) and (11. 6 , 0) and passing through
( 6 , 99). b. 0 < x < 9; the side length of the square
window must be less than the width of the wall,
c. 54 < y < 135; as the side length of the window
increases from 0 to 9, the area of the wall without the
window decreases from 135 to 54. 51. I 53. F
55. 3r(5r+ 1)(2r+ 3) 56. (3qr 2 - 2)(5q - 6 )
57. (7b 3 + 1 )(b + 2) 58. 0.75 59. -0.4 60. - |
61. £ 6 2 .1 6 3 .- 2
Lesson 9-2
- 2 s; 69 ft; 5 < b < 69
Lesso n Ch eck
pp. 553-558
b. Answers may vary.
Sample: It is easy to
evaluate a quadratic
function in the form
y = ax2 + bx + c when
x= 0.