Download review: quadratics

Name __________________________________ Date _________________ Period _________
Unit 6 Review – Quadratics Functions
NON-CALCULATOR
State the domain and range and determine if the relation is a function.
1.
{(1, -4), (2, -3), (3, -4), (4, -3), (5, -4)}
2.
{(0, 2), (1, -3), (0, -2), (2, 2)}
Domain: ___________________
Domain: ____________________
Range: ____________________
Range: _____________________
Function: yes or no
Function: yes or no
3.
4.
Domain: ___________________
Domain: ___________________
Range: ____________________
Range: ____________________
Function: yes or no
Function: yes or no
5.
6.
Domain: ___________________
Domain: ___________________
Range: ____________________
Range: ____________________
Function: yes or no
Function: yes or no
Review Unit 6
Find the indicated value of f(x).
7.
f(x) = 2x2 –x + 1; f(-2) =
8.
f(x) = -3x - 8; f(3) =
Analyze and graph the following quadratic functions. Include your Axis of Symmetry on the graph.
9.
y = 3(x + 3)(x + 3)
x
y
x
y
x
y
Vertex
Axis of Symmetry
Max or Min Value
Domain:
Range:
Roots:
*Vertex Form: _________________
10.
y = -2(x + 6)2 + 2
Vertex
Axis of Symmetry
Max or Min Value
Domain:
Range:
Roots:
*Root Form: ___________________
11.
y = -x2 + 4x + 5
Vertex
Axis of Symmetry
Max or Min Value
Domain:
Range:
Roots:
*Vertex Form: _________________
*Root Form: __________________
Use the following information to write an equation for the quadratic function.
12. roots: -4, 1 f(5) = 16
13. vertex: (-3, 1) f(4) = -13
14. Use root form
Review Unit 6
15. Use vertex form
f(1) = -4
f(2) = -5
Describe the following transformations on the function y = x2.
16. y = 2(x - 1) 2
17. y = -x2 - 4
18. y = -2(x + 3) 2 - 5
19. y =
2
(x - 7) 2 + 2
3
Write the equation for the function y = x2 with the following transformations.
20. shift right 4 and up 2
21. reflect across the x-axis, shift left 2
22. shrink by a factor of
1
, shift left 6 and up 3
2
1
24. If you wanted to shift y = - (x + 6) 2 – 2 up 4
2
and left 3, what would be the new equation?
Review Unit 6
23. Reflect across the x-axis, stretch by a factor
of 2, shift right 8 and down 4
25. If you wanted to shift y = 2x2 - 6 right 3 and
up 7, what would be the new equation?
Review.
26. Solve 5x² - 4x = 2
27. Solve 2x² + x = 15
28. Solve 6x – 3 + 3x = 24
29. Solve 2x² = 32
30. a) Find the equation of the line that contains the point ( -4, 4) and has the same y-intercept as
2x + 3y = 9
b) What is the equation of the line parallel to the line found in part a and has a y-intercept of -5.
Review Unit 6
31. Ellie is landscaping her yard. She wants to buy bushes that cost $19 each and flowers that cost
$6 each. Her budget allows her to spend no more than $200 on this landscaping project. Write an
inequality that could be used to find how many bushes, b, and flowers, f, she could afford.
32. The cost of being a member of Macy’s Health and Fitness Club is an initial fee of $80 plus a
monthly fee of $30. If Joe wants to join the club, how many months could he be a member if he has
budgeted $470 for fees to a fitness club?
33. At a baseball game, Lynn spent $18.50 on 3 cotton candies and 5 soft drinks for her children.
Another parent spent $17.00 on 6 cotton candies and 2 soft drinks. What is the price for 1 cotton
candy and 1 soft drink?
Answers
1. D: {1,2, 3, 4, 5} R: {-4, -3} YES
2. D: {0, 1, 2}; R: {-3, -2, 2} NO
3. D: {-3, 1, 2, 5, 6} R: {-2, 0, 2}
YES
4. D: {-3, 0, 2, 4} R: {-3,-1,2,3,4}
NO
5. D: –9 < x  8; R: –4  y  6;
YES
6. D: x  –6; R: All Real #’s; NO
7. 11
8. –17
9. Vertex: (-3, 0)
Axis of Symmetry: x = -3
Min at y = 0
Domain: All Reals
Range: y  0
Roots: -3 and -3… double root
Points on Graph:(–4,3), (–3,0),
(–2,3)
*Vertex Form: y = 3(x + 3)2
10. Vertex: (-6, 2)
Axis of Symmetry: x = -6
Max at y = 2
Domain: All Reals
Range: y  2
Roots: -5 and -7
Points on Graph: (–8,–6),(-7,0),
(-6,2),(-5,0),-4,-6)
*Root Form: y = -2(x + 7)(x + 5)
11. Vertex: (2, 9)
Axis of Symmetry: x = 2
Max at y = 9
Domain: All Reals
Range: y  9
Roots: -1 and 5
Points on Graph: (0,5),(1,8),
(2,9),(3,8),(4,5)
*Vertex Form: y = –(x – 2)2 + 9
*Root Form: y = –(x + 1)(x + 5)
4
12. y = (x + 4)(x – 1)
9
2
13. y =  (x + 3)2 + 1
7
14. y = (x + 1)(x – 3)
15. y = –(x + 1) 2 + 4
16. stretch by factor of 2,
horizontal translation 1 unit to
right
17. reflected across the x-axis,
vertical translation 4 units
down
18. reflected across the x-axis,
stretch by factor of 2,
horizontal translation 3 units to
left, vertical translation 5 units
down
19. shrink by factor of
2
,
3
horizontal translation 7 units to
right, vertical translation 2 units
up
20. y = (x – 4)2 + 2
21. y = -(x + 2)2
1
22. y = (x + 6)2 + 3
2
23. y = -2(x – 8) 2 – 4
24. y = -
1
(x + 9)2 + 2
2
25. y = 2(x – 3)2 + 1
26.
2  14
5
27.
5
, 3
2
28. 3
29. 4
1
x3
4
1
b) y =  x  5
4
31. 19b + 6f < 200
32. 13 months
33. $4.50 for one of each
30. a) y = 