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Inequalities & Systems Test

Last updated about 6 years ago

20 questions

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Question 20

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A system of equations is shown below:

Y = x2 + 2x + 8
Y = -4x

What is the smallest value of y in the solution set of the system?

16

-2

8

-4

The graph of f(x) = 2x2 - 3x + 5 is shifted down 8 units, producing the graph of q(x).  

Which equation represents the new equation q(x)?

2x2 - 3x + 13

2x2 - 11x + 5

2x2 - 3x - 3

2x2 + 5x + 5

Which function is equivalent to y = x2 - 6x + 10?

y = (x - 3)2 + 1

y = (x + 3)2 - 1

y = (x - 6)2 + 10

y = (x + 6)2 - 10

Solve the following inequality:

2(x - 3) - 5x ≤ 9

x ≤ −1

x ≥  1

x ≥  -5

x ≤  -5

Solve for x:

7(x + 3) - 5x < 13

x < 17

x < -4

x > -17

x > -4

Find the solution(s):

y = x2 + 6x + 10
y = -2x - 6 

 (-4, -4)

 (5, 2) and (5, -9)

 (-4, 2)

 (3, 18) and (-4, 15)

Find the solution(s):

y = x2 - 4x + 6
y = x + 2 

 (-1, 1) and (4, 2)

 (1, 4)

 (1, 4) and (3, 6)

 (1, 3) and (4, 6)

Solve for x:

-3x2 + 45 ≥ 6x

 -5 < x < 3

 -5 ≤ x ≤ 3

 x ≤ -5 or x ≥ 3

 x < -5 or x > 3

What is the equation of this graph?

What is the equation of this graph?

What is the range of this function?

 (- ∞, -2 ]

 [ 0, ∞)

 (-∞, 0)

 [ -2, ∞ )

Which of these equations shifts the square root equation left 3 times?

Find the domain and range of the function:

Domain: [-1. ∞) Range: [4, ∞)

Domain: [1, ∞)  Range: (-∞, 4]

Domain: (-∞, ∞)  Range: [-∞, 4]

Domain: [4, ∞) Range: [-1,∞)

Find the solution(s):

y = x2 + 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)

What is the solution to the linear-quadratic system graphed in the picture?

(-3, 2)

(3, 0)

(2, -3) 

(0, 0)

Solve for x:

4x2 - 8x < 77

 -4 < x < 8

 -6 < x < 8

 -3.5 < x < 5.5

 -2.5 < x < 7.5

Solve for x:

2x2 + 5x ≥ 12

 no solution

 (−∞, -4) U (1.5, ∞)

[-4, 1.5] 

 (−∞, -4] U [1.5, ∞)

Solve for x:

3x - x2 > 0

 (−∞, - 3) U (0, ∞)

 (-3, 0)

 (0, 3)

 (−∞, 0) U (3, ∞)

 Solve the quadratic inequality:

 x2 - 4x - 32 < 0

 x < -8,  x > 4

 −4 < x < 8

 x < −4 ,  x > 8

 −8 < x < 4

Convert to Standard Form: 

y = (x+2)2 + 3

 y = x2 + 4x + 3

 y = x2 + 4x + 4

 y = x2 + 4x + 7

 y = x2 + 2x + 3