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Inequalities & Systems Test
By Shelly Nixon
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Last updated almost 6 years ago
20 questions
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Question 1
1.
A system of equations is shown below:
Y = x
2
+ 2x + 8
Y = -4x
What is the smallest value of y in the solution set of the system?
16
-2
8
-4
Question 2
2.
The graph of f(x) = 2x
2
- 3x + 5 is shifted down 8 units, producing the graph of q(x).
Which equation represents the new equation q(x)?
2x
2
- 3x + 13
2x
2
- 11x + 5
2x
2
- 3x - 3
2x
2
+ 5x + 5
Question 3
3.
Which function is equivalent to y = x
2
- 6x + 10?
y = (x - 3)
2
+ 1
y = (x + 3)
2
- 1
y = (x - 6)
2
+ 10
y = (x + 6)
2
- 10
Question 4
4.
Solve the following inequality:
2(x - 3) - 5x ≤ 9
x ≤ −1
x ≥ 1
x ≥ -5
x ≤ -5
Question 5
5.
Solve for x:
7(x + 3) - 5x < 13
x < 17
x < -4
x > -17
x > -4
Question 6
6.
Find the solution(s):
y = x
2
+ 6x + 10
y = -2x - 6
(-4, -4)
(5, 2) and (5, -9)
(-4, 2)
(3, 18) and (-4, 15)
Question 7
7.
Find the solution(s):
y = x
2
- 4x + 6 y = x + 2
(-1, 1) and (4, 2)
(1, 4)
(1, 4) and (3, 6)
(1, 3) and (4, 6)
Question 8
8.
Solve for x:
-3x
2
+ 45 ≥ 6x
-5 < x < 3
-5 ≤ x ≤ 3
x ≤ -5 or x ≥ 3
x < -5 or x > 3
Question 9
9.
What is the equation of this graph?
Question 10
10.
What is the equation of this graph?
Question 11
11.
What is the range of this function?
(- ∞, -2 ]
[ 0, ∞)
(-∞, 0)
[ -2, ∞ )
Question 12
12.
Which of these equations shifts the square root equation left 3 times?
Question 13
13.
Find the domain and range of the function:
Domain: [-1. ∞) Range: [4, ∞)
Domain: [1, ∞) Range: (-∞, 4]
Domain: (-∞, ∞) Range: [-∞, 4]
Domain: [4, ∞) Range: [-1,∞)
Question 14
14.
Find the solution(s):
y = x
2
+ 8x + 16
y = x + 6
(4,2) and (-5,7)
(-2,4) and (-5,1)
(15,19) and (20,16)
(1,-4) and (3,7)
Question 15
15.
What is the solution to the linear-quadratic system graphed in the picture?
(-3, 2)
(3, 0)
(2, -3)
(0, 0)
Question 16
16.
Solve for x:
4x
2
- 8x < 77
-4 < x < 8
-6 < x < 8
-3.5 < x < 5.5
-2.5 < x < 7.5
Question 17
17.
Solve for x:
2x
2
+ 5x ≥ 12
no solution
(−∞, -4) U (1.5, ∞)
[-4, 1.5]
(−∞, -4] U [1.5, ∞)
Question 18
18.
Solve for x:
3x - x
2
> 0
(−∞, - 3) U (0, ∞)
(-3, 0)
(0, 3)
(−∞, 0) U (3, ∞)
Question 19
19.
Solve the quadratic inequality: x
2
- 4x - 32 < 0
x < -8, x > 4
−4 <
x
< 8
x
< −4 ,
x
> 8
−8 <
x
< 4
Question 20
20.
Convert to Standard Form:
y = (x+2)
2
+ 3
y = x
2
+ 4x + 3
y = x
2
+ 4x + 4
y = x
2
+ 4x + 7
y = x
2
+ 2x + 3