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WorksheetsA.7(c) Changes in a,c,d of Quadratics
Total questions: 55
Worksheet time: 28mins
Name
Class
Date
1.
The parent function of all quadratics is f(x) = x2. All quadratics functions create a shape called a parabola.
a)
Ok parabolas, got it.
b)
...
2.
By adding a coefficient in front of x we can change the shape and orientation of the parabola
a)
Parabolas can only get wider
b)
Parabolas can only get narrower
c)
Parabolas can only flip upside down
d)
Parabolas can make each of these 3 changes
3.
Which of the following statements is true for the quadratic equation:
f(x) = 5x2
f(x) = 5x2
a)
It will get wider because the coefficient > 1
b)
It will get narrower because the coefficient > 1
c)
It will get wider because the coefficient < 1
d)
It will get narrower because the coefficient < 1
4.
Which of the following statements is true for the quadratic equation:
f(x) = 1.5x2
f(x) = 1.5x2
a)
It will get wider because the coefficient > 1
b)
It will get narrower because the coefficient > 1
c)
It will get wider because the coefficient < 1
d)
It will get narrower because the coefficient < 1
5.
Which of the following statements is true for the quadratic equation:
f(x) = 0.3x2
f(x) = 0.3x2
a)
It will get wider because the coefficient > 1
b)
It will get narrower because the coefficient > 1
c)
It will get wider because the coefficient < 1
d)
It will get narrower because the coefficient < 1
6.
Which of the following statements is true for the quadratic equation:
f(x) = ⅔x2
f(x) = ⅔x2
a)
It will get wider because the coefficient > 1
b)
It will get narrower because the coefficient > 1
c)
It will get wider because the coefficient < 1
d)
It will get narrower because the coefficient < 1
7.
Which of the following statements is true for the quadratic equation:
f(x) = 7x2
f(x) = 7x2
a)
It will get wider because the coefficient > 1
b)
It will get narrower because the coefficient > 1
c)
It will get wider because the coefficient < 1
d)
It will get narrower because the coefficient < 1
8.
When a coefficient is negative it doesn't affect the shape (wide/narrow) aspect of the parabola, it only flips the parabola upside down.
a)
OK sounds good.
b)
...
9.
Since a negative coefficient doesn't affect the shape (wide/narrow), which equations will get wider because the coefficient < 1?
a)
f(x) = -5x2
b)
f(x) = -1.3x2
c)
f(x) = -13x2
d)
f(x) = -0.5x2
10.
Which of the following statements is true for the quadratic equation:
f(x) = -2x2
f(x) = -2x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
11.
Which of the following statements is true for the quadratic equation:
f(x) = ¾x2
f(x) = ¾x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
12.
Which of the following statements is true for the quadratic equation:
f(x) = 2.5x2
f(x) = 2.5x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
13.
Which of the following statements is true for the quadratic equation:
f(x) = -¾x2
f(x) = -¾x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
14.
Which of the following statements is true for the quadratic equation:
f(x) = ½x2
f(x) = ½x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
15.
Which of the following statements is true for the quadratic equation:
f(x) = 4x2
f(x) = 4x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
16.
Which of the following statements is true for the quadratic equation:
f(x) = -7x2
f(x) = -7x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
17.
Which of the following statements is true for the quadratic equation:
f(x) = -½x2
f(x) = -½x2
a)
It will get wider because the coefficient < 1
b)
It will flip upside down because of the negative and get narrower because the coefficient > 1
c)
It will flip upside down because of the negative and get wider because the coefficient < 1
d)
It will get narrower because the coefficient > 1
18.
By adding a constant behind x we can change the position of the parabola's vertex moving it up, down, left, or right.
a)
OK so + or - numbers just move the vertex
b)
...
19.
Constant's inside the parenthesis
move the parabola
right (x - #)2 or left (x + #)2.
otherwise the parabola
moves up x2 + # or down x2 - #
move the parabola
right (x - #)2 or left (x + #)2.
otherwise the parabola
moves up x2 + # or down x2 - #
a)
Those might be good notes to have
b)
...
20.
So anytime a constant is added, + #, the parabola moves either
a)
Up or Down
b)
Right or Leftt.
c)
Left or up
d)
Down or Right
21.
So anytime a constant is subtracted, - #, the parabola moves either
a)
Up or Down
b)
Right or Left.
c)
Left or up
d)
Down or Right
22.
So anytime a constant is inside parenthesis, ( x ± #)2, the parabola moves either
a)
Up or Down
b)
Right or Left.
c)
Left or up
d)
Down or Right
23.
So anytime a constant is NOT inside parenthesis, x2 ± #, the parabola moves either
a)
Up or Down
b)
Right or Left.
c)
Left or up
d)
Down or Right
24.
Which of the following statements is true for the quadratic equation:
f(x) = x2 + 6
f(x) = x2 + 6
a)
The parabola moves left because there's no parenthesis
b)
The parabola moves left because its inside parenthesis
c)
The parabola moves up because there's no parenthesis
d)
The parabola moves up because it's inside parenthesis
25.
Which of the following statements is true for the quadratic equation:
f(x) = x2 - 3
f(x) = x2 - 3
a)
The parabola moves right because there's no parenthesis
b)
The parabola moves right because its inside parenthesis
c)
The parabola moves down because there's no parenthesis
d)
The parabola moves down because it's inside parenthesis
26.
Which of the following statements is true for the quadratic equation:
f(x) = (x - 9)2
f(x) = (x - 9)2
a)
The parabola moves right because there's no parenthesis
b)
The parabola moves right because its inside parenthesis
c)
The parabola moves down because there's no parenthesis
d)
The parabola moves down because it's inside parenthesis
27.
Which of the following statements is true for the quadratic equation:
f(x) = (x + 4)2
f(x) = (x + 4)2
a)
The parabola moves left because there's no parenthesis
b)
The parabola moves left because its inside parenthesis
c)
The parabola moves up because there's no parenthesis
d)
The parabola moves up because it's inside parenthesis
28.
Technically a vertex can move both left or right & up or down.
For instance f(x) = (x + 2)2 - 5
Would shift left 2 and down 5.
For instance f(x) = (x + 2)2 - 5
Would shift left 2 and down 5.
a)
That seems easy lets try a few of those.
b)
...
29.
So the equation
f(x) = (x + 4)2 - 3
shifts the vertex
f(x) = (x + 4)2 - 3
shifts the vertex
a)
Right 4 and down 3
b)
Right 4 and up 3
c)
Left 4 and down 3
d)
Left 4 and up 3
30.
So the equation
f(x) = (x + 4)2 + 3
shifts the vertex
f(x) = (x + 4)2 + 3
shifts the vertex
a)
Right 4 and down 3
b)
Right 4 and up 3
c)
Left 4 and down 3
d)
Left 4 and up 3
31.
So the equation
f(x) = (x - 4)2 + 3
shifts the vertex
f(x) = (x - 4)2 + 3
shifts the vertex
a)
Right 4 and down 3
b)
Right 4 and up 3
c)
Left 4 and down 3
d)
Left 4 and up 3
32.
So the equation
f(x) = (x - 4)2 - 3
shifts the vertex
f(x) = (x - 4)2 - 3
shifts the vertex
a)
Right 4 and down 3
b)
Right 4 and up 3
c)
Left 4 and down 3
d)
Left 4 and up 3
33.
Finally the function can have both a coefficient & constants.
f(x) = 2(x - 5)2 + 7
Narrower, Right 5, Up 7
f(x) = 2(x - 5)2 + 7
Narrower, Right 5, Up 7
a)
One step at a time I think I can do this
b)
...
34.
f(x) = 3x2 - 5
a)
The parabola gets narrower and the vertex shifts down
b)
The parabola gets narrower and the vertex shifts up
c)
The parabola gets wider and the vertex shifts down
d)
The parabola gets wider and the vertex shifts up
35.
f(x) = 0.8x2 + 5
a)
The parabola gets narrower and the vertex shifts down
b)
The parabola gets narrower and the vertex shifts up
c)
The parabola gets wider and the vertex shifts down
d)
The parabola gets wider and the vertex shifts up
36.
f(x) = ⅝x2 - 2
a)
The parabola gets narrower and the vertex shifts down
b)
The parabola gets narrower and the vertex shifts up
c)
The parabola gets wider and the vertex shifts down
d)
The parabola gets wider and the vertex shifts up
37.
f(x) = 20x2 + 2
a)
The parabola gets narrower and the vertex shifts down
b)
The parabola gets narrower and the vertex shifts up
c)
The parabola gets wider and the vertex shifts down
d)
The parabola gets wider and the vertex shifts up
38.
f(x) = -20x2 + 2
a)
The parabola gets narrower, flips upside down and the vertex shifts left
b)
The parabola gets narrower, flips upside down and the vertex shifts up
c)
The parabola gets wider, flips upside down and the vertex shifts left
d)
The parabola gets wider, flips upside down and the vertex shifts up
39.
Which of the following changes wouldn't occur for the function
f(x) = 2(x + 5)2 - 4
f(x) = 2(x + 5)2 - 4
a)
The parabola gets narrower
b)
The vertex shifts down
c)
The parabola flips upside down
d)
The vertex shifts left
40.
a)
f(x) = (x - 5)2
b)
f(x) = (x + 5)2
c)
f(x) = x2 - 5
d)
f(x) = -5x2
41.
a)
f(x) = (x - 5)2
b)
f(x) = 5x2
c)
f(x) = x2 - 5
d)
f(x) = -5x2
42.
a)
f(x) = ⅕x2
b)
f(x) = 5x2
c)
f(x) = -⅕x2
d)
f(x) = -5x2
43.
a)
f(x) = (x + 5)2
b)
f(x) = 5x2
c)
f(x) = x2 + 5
d)
f(x) = (x + 5)2 + 5
44.
Whats type of change will this function have?
f(x) = 3x2
f(x) = 3x2
a)
narrower / thinner
b)
left / right
c)
up / down
45.
Whats type of change will this function have?
f(x) = (x + 6)2
f(x) = (x + 6)2
a)
narrower / thinner
b)
left / right
c)
up / down
46.
Whats type of change will this function have?
f(x) = x2 - 7
f(x) = x2 - 7
a)
narrower / thinner
b)
left / right
c)
up / down
47.
Whats type of change will this function have?
f(x) = ⅞x2
f(x) = ⅞x2
a)
narrower / thinner
b)
left / right
c)
up / down
48.
Whats type of change will this function have?
f(x) = x2 + 8
f(x) = x2 + 8
a)
narrower / thinner
b)
left / right
c)
up / down
49.
Whats type of change will this function have?
f(x) = (x - 11)2
f(x) = (x - 11)2
a)
narrower / thinner
b)
left / right
c)
up / down
50.
Whats type of changes will this function have?
f(x) = 3x2 + 7
f(x) = 3x2 + 7
a)
It gets narrower because 3 > 1 and shifts up because of the + 7
b)
It gets narrower because 3 > 1 and shifts left because of the + 7
c)
It gets wider because 3 > 1 and shifts up because of the + 7
d)
It gets wider because 3 > 1 and shifts left because of the + 7
51.
Whats type of changes will this function have?
f(x) = 0.3x2 + 7
f(x) = 0.3x2 + 7
a)
It gets narrower because 0.3 < 1 and shifts up because of the + 7
b)
It gets narrower because 0.3 < 1 and shifts left because of the + 7
c)
It gets wider because 0.3 < 1 and shifts up because of the + 7
d)
It gets wider because 0.3 < 1 and shifts left because of the + 7
52.
Whats type of changes will this function have?
f(x) = 3(x + 7)2
f(x) = 3(x + 7)2
a)
It gets narrower because 3 > 1 and shifts up because of the + 7
b)
It gets narrower because 3 > 1 and shifts left because of the + 7
c)
It gets wider because 3 > 1 and shifts up because of the + 7
d)
It gets wider because 3 > 1 and shifts left because of the + 7
53.
Whats type of changes will this function have?
f(x) = 0.3(x + 7)2
f(x) = 0.3(x + 7)2
a)
It gets narrower because 0.3 < 1 and shifts up because of the + 7
b)
It gets narrower because 0.3 < 1 and shifts left because of the + 7
c)
It gets wider because 0.3 < 1 and shifts up because of the + 7
d)
It gets wider because 0.3 < 1 and shifts left because of the + 7
54.
a)
f(x) = -0.1x2
f(x) = x2 - 4
f(x) = (x - 6)2
f(x) = x2 - 4
f(x) = (x - 6)2
b)
f(x) = -0.1x2
f(x) = x2 - 4
f(x) = (x + 6)2
f(x) = x2 - 4
f(x) = (x + 6)2
c)
f(x) = -0.1x2
f(x) = x2 + 4
f(x) = (x - 6)2
f(x) = x2 + 4
f(x) = (x - 6)2
d)
f(x) = 0.1x2
f(x) = x2 - 4
f(x) = (x - 6)2
f(x) = x2 - 4
f(x) = (x - 6)2
55.
Which of the following statements is true.
a)
Coefficients can only change narrow/ wide and constants change up, right, left, & down.
b)
Constants can only change narrow/ wide and coefficients change up, right, left, & down.
c)
Coefficients can change narrow, wide and/or flip and constants change up, right, left, & down.
d)
Constants can change narrow, wide and/or flip and coefficients change up, right, left, & down.
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