Lesson Practice 35 a.
Lesson Warm Up 35
35
e. -4 and 2 are the roots of the equation, the zeros of the related function f(x) = x2 + 2x - 8, and the x-intercepts of the graph.
1. quadratic 2. 4x(2x + 1) 3. 2(4x + 1)(2x - 3)
y
Lesson Practice 35
x -2
1 1 and _ a. - _ 5 5
-2
b. 0 and 7
-6
-4
-8
2 and 1 c. - _ 3
f(x) = x 2 + 2x
d. -4 is the double root of the equation, the only zero of the related function f(x) = x2 + 8x + 16, and the only x-intercept of the graph.
8
f. Sample: f(x) = 4x2 + 17x - 15 g. 2.5 seconds
y 6 4 2 x -6 -4 -2 f(x) = x 2 + 8x + 16
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–1
Saxon Algebra 2
Lesson Practice 35
35
13. The line has no slope, or an undefined slope. It does not have a zero slope. A horizontal line has a zero slope.
3 c _ 1. 6
b
a2 _ 2. 8 2 8x y
16 3. -_ 9
14. only 4
4. x = -28 or x = 2
15. The given multiplication expression is undefined when x = 4.
5. y = -x + 1 6. (2, 3) 7. (-1, 2) 8. a = 102, b = 38 9. f (x) · g (x) = (4x - 3)(8x + 9) = 32x2 + 12x - 27 10. See student work. A continuous function can be drawn without lifting the pencil from the paper.
16. Possible answer: Factor a2 - 8a + 16 to (a - 4)(a - 4). Area is length multiplied by width, and each side length is a - 4. The side length along the x-axis is the difference between the x values. So, a - 4 = x - (a - 1). Then, x = 2a - 5. So, a possible adjacent vertex is (2a - 5, 0).
11. C 1 12. _ 144
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–2
Saxon Algebra 2
Lesson 17. Possible answer: The equation 1 y+1=_ (x - 2) is a 4 linear equation in the point-slope form y - y1 = m(x - x1). So its graph is a line, (x 1, y 1) = (2, -1) is a point on the line, and 1 m=_ is the slope of 4 the line.
24. Possible description: Stretch (dilate) the graph of y = x vertically by a factor of 1.2563 25. B 26. y = 5.51x - 144.94 27. D 28. 110 grams of spaghetti, 56 grams of ground beef, 34 grams of tomato sauce
18. 4 < x ≤ 10; 0
2
4
6
8
10
12
16t2 + 8t 19. a. _ = 16t + 8 t
29. x(1.9x) = 17.1 1.9x2 = 17.1 1.9x2 17.1 _ =_
b. 48 feet per second
1.9
20. 5.25 liters of the 15% solution and 1.75 liters of the 35% solution
1.9
x2 = 9 x = -3 or x = 3 Choose the positive solution. x = 3 and 1.9x = 5.7. The dimensions are 3 feet and 5.7 feet.
21. 0, 1, or 2 real zeros; The number of real zeros is the number of points in which the graph intersects the x-axis. 22. direct
35
30. 3 ft.
23. 6
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–3
Saxon Algebra 2
35
e. -4 and 2 are the roots of the equation, the zeros of the related function f(x) = x2 + 2x - 8, and the x-intercepts of the graph.
1. quadratic 2. 4x(2x + 1) 3. 2(4x + 1)(2x - 3)
y
Lesson Practice 35
x -2
1 1 and _ a. - _ 5 5
-2
b. 0 and 7
-6
-4
-8
2 and 1 c. - _ 3
f(x) = x 2 + 2x
d. -4 is the double root of the equation, the only zero of the related function f(x) = x2 + 8x + 16, and the only x-intercept of the graph.
8
f. Sample: f(x) = 4x2 + 17x - 15 g. 2.5 seconds
y 6 4 2 x -6 -4 -2 f(x) = x 2 + 8x + 16
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–1
Saxon Algebra 2
Lesson Practice 35
35
13. The line has no slope, or an undefined slope. It does not have a zero slope. A horizontal line has a zero slope.
3 c _ 1. 6
b
a2 _ 2. 8 2 8x y
16 3. -_ 9
14. only 4
4. x = -28 or x = 2
15. The given multiplication expression is undefined when x = 4.
5. y = -x + 1 6. (2, 3) 7. (-1, 2) 8. a = 102, b = 38 9. f (x) · g (x) = (4x - 3)(8x + 9) = 32x2 + 12x - 27 10. See student work. A continuous function can be drawn without lifting the pencil from the paper.
16. Possible answer: Factor a2 - 8a + 16 to (a - 4)(a - 4). Area is length multiplied by width, and each side length is a - 4. The side length along the x-axis is the difference between the x values. So, a - 4 = x - (a - 1). Then, x = 2a - 5. So, a possible adjacent vertex is (2a - 5, 0).
11. C 1 12. _ 144
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–2
Saxon Algebra 2
Lesson 17. Possible answer: The equation 1 y+1=_ (x - 2) is a 4 linear equation in the point-slope form y - y1 = m(x - x1). So its graph is a line, (x 1, y 1) = (2, -1) is a point on the line, and 1 m=_ is the slope of 4 the line.
24. Possible description: Stretch (dilate) the graph of y = x vertically by a factor of 1.2563 25. B 26. y = 5.51x - 144.94 27. D 28. 110 grams of spaghetti, 56 grams of ground beef, 34 grams of tomato sauce
18. 4 < x ≤ 10; 0
2
4
6
8
10
12
16t2 + 8t 19. a. _ = 16t + 8 t
29. x(1.9x) = 17.1 1.9x2 = 17.1 1.9x2 17.1 _ =_
b. 48 feet per second
1.9
20. 5.25 liters of the 15% solution and 1.75 liters of the 35% solution
1.9
x2 = 9 x = -3 or x = 3 Choose the positive solution. x = 3 and 1.9x = 5.7. The dimensions are 3 feet and 5.7 feet.
21. 0, 1, or 2 real zeros; The number of real zeros is the number of points in which the graph intersects the x-axis. 22. direct
35
30. 3 ft.
23. 6
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 35–3
Saxon Algebra 2
