-4 -3 -2 -1 1 2 3 4

-4

-3

-2

-1

1

2

3

4

x

y

Quadratics Test Review

x y-2 -130 72 -134 -736 -173

1. Linear or Quadratic

+2

+2

+2

+2

+20

-20

-60

-100

+40

+40

+40

0

0

0

x y-2 -37-1 -230 -91 52 19

2. Linear or Quadratic

+1

+1

+1

+1

+14

+14

+14

+14

x y-2 10-1 -20 -61 -22 10

3. Linear or Quadratic

+1

+1

+1

+1

-12

-4

+4

+12

+8

+8

+8

0

0

0

4. Linear or Quadratic

-3x + 4y = 8

5. Linear or Quadratic

y = -5x2 + 3x – 17

6. Linear or Quadratic

3x2 + 5y = 24

1 1

7. Linear or Quadratic 8. Linear or Quadratic

9. Linear or Quadratic

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Domain: All real numbers

Range: y ≥ -4

10.

Domain: All real numbers

Range: y ≤ 9

11.

Domain: All real numbers

Range: y ≥ -8

12.

x y-2 4-1 -20 -41 -22 4

13. y = 2x2 – 4

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Remember, in the calculator you can create the table of values easily.Go to:

1)[ Y = ] and enter your equation2)[2nd ] [Graph/Table}

x y-2 -1.3-1 -.30 01 -.32 -1.3

14. y = (-1/3)x2

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

x y-2 0-1 -30 -41 -32 0

16. y = x2 - 4

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

16.

a) Label and give the ordered pair of the vertex.( , )

b) Is the vertex the maximum or the minimum?

c) Draw and give the equation of the axis of symmetry.

Equation: _____________

d) Identify the roots. ( , ) ( , )

a) Label and give the ordered pair of the vertex.( , )

b) Is the vertex the maximum or the minimum?

c) Draw and give the equation of the axis of symmetry.

Equation: _____________

d) Identify the roots. ( , ) ( , )

17.

a) Label and give the ordered pair of the vertex.( , )

b) Is the vertex the maximum or the minimum?

c) Draw and give the equation of the axis of symmetry.

Equation: _____________

d) Identify the roots. ( , ) ( , )

18.

19. Vertex: (2, 4) and two zeros

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

20. Vertex: (2, 4) and no roots

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

21. One x-intercept

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

22. y = 5x2 + 3Domain: {-3, 1, 3, 5}

Range: 5(-3)2 + 3 = 5(1)2 + 3 = 5(3)2 + 3 = 5(5)2 + 3 =

48848128 {8, 48, 128}

OR you could create the table of values in the calculatorGo to:

1)[ Y = ] and enter your equation2)[2nd ] [Graph/Table}

23. y = -2x2 + 4x – 7 Domain: {-1, 0, 3, 4}

Range:

{-23, -13, -7}

x y-1 -130 -73 -134 -23

24. y = -17x + 8 Domain: {0, 1, 2, 5}

Range:

{-77, -26, -9, 8}

x y0 81 -92 -265 -77

25. f(x) = 4x – 1

f(-3) = 4(-3) – 1

f(-3) = -13

26. f(x) = 2x² – 16

f(-2) = 2(-2)² – 16

f(-2) = -8

27. f(x) = (1/3)x² + 9

f(6) = (1/3)(6)² + 9

f(6) = 21

_____ 28. Which of the following functions represents a parabola that is narrower than the parent function f(x) = x2 ?

A.f(x) = x2 + 3 B. f(x) = ⅓ x2

C. f(x) = 3x2 D. f(x) = x2 – 3

Remember:The larger the coefficient, the narrowerThe smaller the coefficient, the wider

_____ 29. How do the graphs of the functions f(x) = x2 + 5 and g(x) = x2 − 6 relate to each other?

A.The graph of f(x) is one unit above the graph of g(x).

B.The graph of f(x) is 11 units above the graph of g(x).

C.The graph of f(x) is one unit to the right the graph of g(x).

D.The graph of f(x) is 11 units to the right the graph of g(x).

_____ 30. When graphed, which function would be shifted 3 units down from the graph of f(x) = x2 + 6?

A.g(x) = x2 + 9

B.g(x) = x2 + 3

C.g(x) = x2 – 3

D.g(x) = x2 + 1

_____ 31. Given the function y = x2 + 3, which describes the shift in the vertex of the parabola if, in the function, 3 is changed to -8?

A.5 units down

B.5 units up

C.11 units up

D.11 units down

_____ 32. How would the graph of the function y=x2 – 4 be affected if the function were changed to y=x2 + 1?

A. The graph would shift 5 units down.

B. The graph would shift 5 units up.

C. The graph would shift -3 units down.

D. The graph would shift 3 units up.

33. Order the functions from narrowest to widest.

f(x) = - ½ x2 , g(x) = 3x2 , h(x) = -2x2

g(x) = 3x2 , h(x) = -2x2, f(x) = - ½ x2

34. How do the graphs of the functions f(x) = x2 − 4 and g(x) = x2 + 2 relate to each other?

f(x) is 6 units below g(x) OR

g(x) is 6 units above f(x)

35.Write the equation of the function that is shifted 3 units above the function y = x2 + 2.

y = x2 + 5

36.Describe the change from the parent function y = x2 to y = 5x2 – 8.

y = 5x2 – 8 is narrower and is 8 units below y = x2

Time Height012345678910

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y

Scott shot his algebra book using a giant slingshot. The path of the book can be modeled by the function y = -16x2 + 160x.

37. 38.Time Height0 01 1442 2563 3364 3845 4006 3847 3368 2569 14410 0 40

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y

39.What ordered pair represents when the book reaches its maximum height? ( ___,___)

40.How long did it take for the book to hit the ground?

_____________

41.At what times was the book at 336 feet?

_____________

42.What does the ordered pair (8, 256) represent?

__________________________________

5 400

40

80

120

160

200

240

280

320

360

400

10 seconds

3 and 7 seconds

After 8 seconds, the book is 256 feet high