unit 6 test review answer key - andrewmoschetti.com€¦ · answer key (4) this problem can be ......

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COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #6 eMATH INSTRUCTION , RED HOOK , NY 12571, © 2015

UNIT 6 TEST REVIEW ANSWERS QUADRATIC FUNCTIONS AND THEIR ALGEBRA

Part I Questions 1. For the function ( ) 2 2 15f x x x= − − , over which of the following intervals is ( ) 0f x > always?

(1) 0x > (3) 5 or 3x x< − > (2) 0x < (4) 3 or 5x x< − >

2. The function ( )216 17

2y x= − − + is strictly decreasing over which of the following intervals

(1) 6x > (3) 3x > (2) 6x < (4) 17x < 3. The height of an object can be modeled by the equation 2( ) 16 48h t t t= − + . Which of the following is not an

equivalent way of expressing this function?

(1) ( ) ( )216 3h t t t= − − (3) ( ) ( )16 48h t t t= − −

(2) ( ) ( )4 4 12h t t t= − − (4) ( ) ( )16 3h t t t= −

4. Which of the following is not a factor of the expression 33 75x x− ? (1) 5x + (3) 3x (2) 3x + (4) 2 25x −

Answer Key

(4)

This problem can be done in a variety of ways. But, it is likely easiest to place the function into a calculator and inspect values. We find that Choice (4), when

and when , the function will have positive outputs.

(1)

This parabola has a turning point at and opens

downward. Thus, it must be decreasing for all values of x that are greater than 6.

(2)

(2)

Check each choice by multiplying out the factors to see if they result in the original function. We can see from Choice (2):


5. The trinomial 24 3 10x x− − can be written equivalently as (1) ( )( )2 5 2 2x x− + (3) ( ) ( )4 1 10x x+ −

(2) ( )( )2 1 10x x− + (4) ( )( )4 5 2x x+ −

6. The cubic polynomial 3 23 5 12 20x x x+ + + can be factored as

(1) ( ) ( )23 5 2x x+ + (3) ( )( )5 3 2x x+ +

(2) ( ) ( )23 5 4x x+ + (4) ( ) ( ) ( )5 2 2x x x+ − +

7. The polynomial 22 4 3 6x ax bx ab− + − can be written as (1) ( ) ( )2 2 3x a x b− + (3) ( )( )2 3 2 2x b x b− +

(2) ( )( )2 2 3x b x a+ − (4) ( ) ( )2 6x a x b− +

8. The equation 5�� 7��3� � 2� has a solution set of

(1) 2

5, , 73

− − ±

(3) 2

, 0, 73

−

(2) { }5, 2, 7− − (4) { }2, 0, 7− ±

(4)

Multiply each of the following pairs of binomials to see which is equivalent to the original trinomial. Choice (4) gives:

(2)

Note: Since is the sum of perfect squares (and no the difference), it cannot be factored.

(1)

(3)


9. The quadratic function ( ) 210 11 6f x x x= + − has one zero at 3

2x = − . At which of the following x-values is

its other zero?

(1) 6x = (3) 1

6x =

(2) 2

5x = (4) 4x = −

10. Which of the following is the solution set to the inequality 2 6 16 0x x− − < ? (1) 2 8x− < < (3) 4 4x− < < (2) 8x > (4) 16x < − 11. What is the x-coordinate of the turning point of the parabola 25 27 3y x x= + − ? (1) 2.7x = − (3) 5.4x = (2) 1.8x = − (4) 7.2x = 12. The parabola 23 24 55y x x= − + can be written in the form

(1) ( )23 2 2y x= − + (3) ( )2

3 2 11y x= + −

(2) ( )23 8 55y x= − + (4) ( )23 4 7y x= − +

Since is a zero, then must be a factor of

this polynomial. But, this means it must factor as:

Which means its other zero must be

(2)

(1) (+) (+) (-)

(1)

(4)


13. A cable hangs in a parabolic shape above a level surface between two poles such that its height above the surface is given by the equation 2.001 .124 16y x x= − + , where y is the cable's height above the surface, in feet, and x is the horizontal distance from one of the poles. According to this model, which of the following represents the lowest height the cable is above the surface?

(1) 8.9 feet (3) 11.3 feet (2) 10.1 feet (4) 12.2 feet 14. A circle whose center is at ( )5, 3− and which passes through the point ( )7, 8− has a radius equal to

(1) 5 (3) 44

(2) 29 (4) 8 15. A circle whose equation is 2 24 10 12 0x x y y+ + − + = has a center at (1) ( )2, 5− (3) ( )4,10−

(2) ( )3, 8− (4) ( )2, 6

16. A parabola has a focus at ( )0,10 and a directrix of the x-axis. Which of the following is the equation of the

parabola?

(1) 2 10y x= + (3) 215

5y x= − +

(2) 215

10y x= + (4) 21

520

y x= +

(4)

(2)

(1)

(4)


Free Response 17. Factor the expression below completely.

3 212 20 3 5x x x+ − −

18. Given ( ) 22 13 36f x x x= − + , algebraically find all values of x that solve the equation ( ) 15f x = .

19. Find the x coordinates where the line 3 2y x= − intersects the circle 2 2 116x y+ = . Only an algebraic solution

is acceptable. 20. Find all zeroes of the function f(x) = x2 – 4x – 5. Justify your answer algebraically.


21. Algebraically determine the solution to the inequality below. Plot its solution on the number line provided. 2 2 35 0x x+ − > 22. Place the following quadratic function in vertex form. Identify the coordinates of its turning point. � �� 8� � 15

23. Determine the center and radius of the circle whose equation is

2 26 14 42x x y y+ + − =

Test values of x in the inequality in each portion of the number line using and as the dividing points of the number line.

(+) (+) (-)

� �� 8� � 16 � 16 � 15 � �� 4�� 1

Turning Point ��4,�1�


24. A parabola has a focus at ( )6, 8 and a directrix of 2y = .

(a) Create a rough sketch of the parabola on the axes below. Label the focus and directrix (b) What are the coordinates of the vertex of the parabola?

�6,5� (c) Determine the equation of the parabola using the locus definition of a parabola.

(((( )))),x y

Name: ____________________________________ Date: ___________________ CC Algebra 2


UNIT 6 TEST REVIEW QUADRATIC FUNCTIONS AND THEIR ALGEBRA

Part I Questions 1. For the function ( ) 2 2 15f x x x= − − , over which of the following intervals is ( ) 0f x > always?

(1) 0x > (3) 5 or 3x x< − > (2) 0x < (4) 3 or 5x x< − >

2. The function ( )216 17

2y x= − − + is strictly decreasing over which of the following intervals

(1) 6x > (3) 3x > (2) 6x < (4) 17x < 3. The height of an object can be modeled by the equation 2( ) 16 48h t t t= − + . Which of the following is not an

equivalent way of expressing this function?

(1) ( ) ( )216 3h t t t= − − (3) ( ) ( )16 48h t t t= − −

(2) ( ) ( )4 4 12h t t t= − − (4) ( ) ( )16 3h t t t= −

4. Which of the following is not a factor of the expression 33 75x x− ? (1) 5x + (3) 3x (2) 3x + (4) 2 25x −


5. The trinomial 24 3 10x x− − can be written equivalently as (1) ( )( )2 5 2 2x x− + (3) ( )( )4 1 10x x+ −

(2) ( )( )2 1 10x x− + (4) ( ) ( )4 5 2x x+ −

6. The cubic polynomial 3 23 5 12 20x x x+ + + can be factored as

(1) ( )( )23 5 2x x+ + (3) ( )( )5 3 2x x+ +

(2) ( )( )23 5 4x x+ + (4) ( ) ( ) ( )5 2 2x x x+ − +

7. The polynomial 22 4 3 6x ax bx ab− + − can be written as (1) ( ) ( )2 2 3x a x b− + (3) ( )( )2 3 2 2x b x b− +

(2) ( )( )2 2 3x b x a+ − (4) ( )( )2 6x a x b− +

8. The equation5�� − 7��3� + 2� has a solution set of

(1) 2

5, , 73

− − ±

(3) 2

, 0, 73

−

(2) { }5, 2, 7− − (4) { }2, 0, 7− ±


9. The quadratic function ( ) 210 11 6f x x x= + − has one zero at 3

2x = − . At which of the following x-values is

its other zero?

(1) 6x = (3) 1

6x =

(2) 2

5x = (4) 4x = −

10. Which of the following is the solution set to the inequality 2 6 16 0x x− − < ? (1) 2 8x− < < (3) 4 4x− < < (2) 8x > (4) 16x < − 11. What is the x-coordinate of the turning point of the parabola 25 27 3y x x= + − ? (1) 2.7x = − (3) 5.4x = (2) 1.8x = − (4) 7.2x = 12. The parabola 23 24 55y x x= − + can be written in the form

(1) ( )23 2 2y x= − + (3) ( )23 2 11y x= + −

(2) ( )23 8 55y x= − + (4) ( )23 4 7y x= − +


13. A cable hangs in a parabolic shape above a level surface between two poles such that its height above the surface is given by the equation 2.001 .124 16y x x= − + , where y is the cable's height above the surface, in feet, and x is the horizontal distance from one of the poles. According to this model, which of the following represents the lowest height the cable is above the surface?

(1) 8.9 feet (3) 11.3 feet (2) 10.1 feet (4) 12.2 feet 14. A circle whose center is at ( )5, 3− and which passes through the point ( )7, 8− has a radius equal to

(1) 5 (3) 44

(2) 29 (4) 8 15. A circle whose equation is 2 24 10 12 0x x y y+ + − + = has a center at (1) ( )2, 5− (3) ( )4,10−

(2) ( )3, 8− (4) ( )2, 6

16. A parabola has a focus at ( )0,10 and a directrix of the x-axis. Which of the following is the equation of the

parabola?

(1) 2 10y x= + (3) 215

5y x= − +

(2) 215

10y x= + (4) 21

520

y x= +


Free Response 17. Factor the expression below completely.

3 212 20 3 5x x x+ − − 18. Given ( ) 22 13 36f x x x= − + , algebraically find all values of x that solve the equation ( ) 15f x = .

19. Find the x coordinates where the line 3 2y x= − intersects the circle 2 2 116x y+ = . Only an algebraic solution

is acceptable. 20. Find all zeroes of the function f(x) = x2 – 4x – 5. Justify your answer algebraically.


21. Algebraically determine the solution to the inequality below. Plot its solution on the number line provided. 2 2 35 0x x+ − > 22. Place the following quadratic function in vertex form. Identify the coordinates of its turning point. � = � + 8� + 15 23. Determine the center and radius of the circle whose equation is

2 26 14 42x x y y+ + − =


24. A parabola has a focus at ( )6, 8 and a directrix of 2y = .

(a) Create a rough sketch of the parabola on the axes below. Label the focus and directrix (b) What are the coordinates of the vertex of the parabola? (c) Determine the equation of the parabola using the locus definition of a parabola.

unit 6 test review answer key - andrewmoschetti.com€¦ · answer key (4) this problem can be ......

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