Name _________________________________________________ Date ____________________ Block _________

1.1 Assignment – Solving Multi-Step Equations

Solve the following multi-step equations. Check your solution.

1. 10𝑠 + 2𝑠 + 3𝑠 + 4 = 34 Check Solution

2. 5(𝑥 + 2) = 4(𝑥 − 2) Check Solution

3. −(5𝑎 + 5) = −6𝑎 Check Solution

4. 4(𝑥 + 3) = 𝑥 + 15 Check Solution

5. 8 − (7𝑠 + 50) = −𝑠 Check Solution

Name ____________________________________________________ Date __________________ Block _________

1.2 Assignment – Absolute Value Equations

Solve the equations and give the solutions verbally, graphically, and using set builder notation.

1. |5𝑥 − 10| = 45 2. |𝑥 − 3| = 10

Verbally: ___________________ Verbally: ___________________

Graphically: Graphically:

Set Builder Notation: _________ Set Builder Notation: _________

3. 4|𝑧 − 1| = 8 4. −2 |𝑚 − 6| = −24

Verbally: ___________________ Verbally: ___________________

Graphically: Graphically:

Set Builder Notation: _________ Set Builder Notation: _________

5. −10|4𝑥 − 2| + 6 = −54 6. |𝑥 − 63| + 5 = 3

Verbally: ___________________ Verbally: ___________________

Graphically: Graphically:

Set Builder Notation: _________ Set Builder Notation: _________

7. Find the error in the following attempt 2|3𝑥 − 1| + 6 = 18

to solve the absolute value equation. |3𝑥 − 1| + 6 = 9

What is/are the correct solution(s)? |3𝑥 − 1| = 3

3𝑥 − 1 = 3 𝑜𝑟 3𝑥 − 1 = −3

3𝑥 = 4 𝑜𝑟 3𝑥 = −2

𝑥 =4

3 𝑜𝑟 𝑥 = −

2

3

Name __________________________________________________ Date __________________ Block ___________

1.3 Assignment – Absolute Value Equations (Day 2)

Solve the absolute value equations. Express the solutions verbally, graphically, and using set builder notation.

1. 5|𝑐 − 2| = 30 2. |−𝑥 + 8| = 2

Verbally: _______________________________ Verbally: _______________________________

Graphically: Graphically:

Set Builder Notation: _____________________ Set Builder Notation: _____________________

3. |3𝑥 − 1| + 5 = 3 4. 2|𝑥 − 3| − 7 = 1

Verbally: _______________________________ Verbally: _______________________________

Graphically: Graphically:

Set Builder Notation: _____________________ Set Builder Notation: _____________________

Name ______________________________________________ Date __________________ Block ________

1.4 Assignment – Graphing Linear Equations

Graph each equation. Give 3 points on the line.

1. Plot 12 −= xy

Slope: ______

𝑦-intercept: ______

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

2. Plot 82

5+−= xy

Slope: ______

𝑦-intercept: ______

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

3. Plot 2+= xy

Slope: ______

𝑦-intercept: ______

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

4. Plot 54

1+−= xy

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

5. Plot 24

3−= xy

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

6. Plot 15 −−= xy

Give the coordinates of 3 points on the line.

(_____, _____), (_____, _____). (_____, _____)

Name __________________________________________________ Date __________________ Block ___________

1.5 Assignment – Graphing Absolute Value Equations

Graph the following absolute value functions.

1. 31 −+= xy 2. 12

1−= xy 3. 1

3

1+−= xy

Vertex: (___,___) Vertex: (___,___) Vertex: (___,___)

a = _______ a = _______ a = _______

y-intercept: ________ y-intercept: ________ y-intercept: ________

Min or Max: ________ Min or Max: ________ Min or Max: ________

X

Y

X

Y

X

Y

4. 122 ++= xy 5. 2−−= xy 6. xy2

3−=

Vertex: (___,___) Vertex: (___,___) Vertex: (___,___)

a = _______ a = _______ a = _______

y-intercept: ________ y-intercept: ________ y-intercept: ________

Min or Max: ________ Min or Max: ________ Min or Max: ________

X

Y

X

Y

X

Y

Name __________________________________________________ Date __________________ Block ___________

ERROR ANALYSIS JIGSAW

Find and circle the error in each problem. Then, explain the mistake and work or graph the problem correctly.

1. Solve for 𝑥: 2(3𝑥 − 4) = 16 Correction: 2(3𝑥 − 4) = 16

6𝑥 − 2 = 16

+2 + 2

6𝑥 = 18

6 6

𝑥 = 3

Explain the error: ___________________________________________________________________________________

__________________________________________________________________________________________________

__________________________________________________________________________________________________

2. Graph the equation: 𝑦 = 3𝑥 − 4 Correction: 𝑦 = 3𝑥 − 4

Explain the error: ___________________________________________________________________________________

__________________________________________________________________________________________________

__________________________________________________________________________________________________

3. Solve for 𝑥: −2|𝑥 + 9| − 3 = 7 Correction: −2|𝑥 + 9| − 3 = 7

+3 + 3

−2 |𝑥 + 9| = 10

−2 −2

|𝑥 + 9| = −5

𝑥 + 9 = −5 𝑥 + 9 = 5

−9 − 9 −9 − 9

𝑥 = −14 𝑥 = −4

Explain the error: ___________________________________________________________________________________

__________________________________________________________________________________________________

__________________________________________________________________________________________________

4. Graph the equation: 𝑦 = |𝑥 − 5| − 2 Correction: 𝑦 = |𝑥 − 5| − 2

Explain the error: ___________________________________________________________________________________

__________________________________________________________________________________________________

__________________________________________________________________________________________________

Name _______________________________________________ Date ____________________ Block ___________

AFDA – Unit 1 Test Review

Solve the absolute value equations.

1. |𝑥 − 5| = 6 2. 2|𝑥 + 4| = 18

Verbally: _____________________________ Verbally: _____________________________

Graphically: Graphically:

Set Builder: ___________________________ Set Builder: ___________________________

3. |6 + 𝑥| = −5 4. 2|𝑥 − 3| + 10 = 10

Verbally: _____________________________ Verbally: _____________________________

Graphically: Graphically:

Set Builder: ___________________________ Set Builder: ___________________________

Graph each of the following absolute value equations.

5. 𝑦 = −2

5|𝑥 − 1| 6. 𝑦 = −2|𝑥| + 3

Interpret the following graphs.

7. Give the coordinates of the y-intercept. _______

8. Give the coordinates of the absolute minimum, if it exists. _______

9. Give the coordinates of the absolute maximum, if it exists. _______

10. Write an equation for the graph. ____________________________

11. Give the coordinates of the y-intercept. _______

12. Give the coordinates of the absolute minimum, if it exists. _______

13. Give the coordinates of the absolute maximum, if it exists. _______

14. Write an equation for the graph. ____________________________

Name _________________________________________________ Date ________________ Block ______

2.1 Assignment – Operations on Polynomials

Add the following polynomials.

1. (3𝑥2 − 5𝑥 + 7) + (𝑥2 + 8𝑥 − 3) 2. (4𝑎5 + 3𝑎 − 5) + (2𝑎5 − 𝑎3 + 2)

Subtract the following polynomials.

3. (3𝑥2 − 5𝑥 + 7) − (𝑥2 + 8𝑥 − 3) 4. (4𝑟3 + 3𝑟2 − 2) − (𝑟3 + 3𝑟 − 5)

Multiply the following polynomials. 5. (3𝑥 − 5)(𝑥 + 2) 6. (𝑥2 − 3)(3𝑥2 + 4𝑥 − 7)

Name ________________________________________ Date ___________________ Block _______

2.2 Assignment – Analyzing Graphs of Quadratic Equations

Perform the indicate operation.

1. (−2𝑥2 + 5𝑥 − 1) + (−3𝑥3 − 4𝑥 + 2) 2. (6𝑥3 + 7𝑥2 + 3) − (5𝑥2 + 4𝑥 − 2)

3. (𝑥 + 3)(2𝑥2 + 4𝑥 − 1)

Answer the question for each graph.

4. 5.

a) Label the vertex: _______________ a) Label the vertex: _______________

b) This graph opens up / down , b) This graph opens up / down ,

so 𝑎 must be positive / negative. so 𝑎 must be positive / negative.

c) Possible equation: _______________ c) Possible equation: ______________

d) Label the Solution(s): _____________ d) Label the root(s): _______________

e) Label the 𝑦-intercept: ____________ e) Label the 𝑦-intercept: ___________

f) This graph rises / falls to the right. f) This graph rises / falls to the right.

g) This graph has a minimum / maximum g) This graph has a minimum / maximum

6. 7.

a) Label the vertex: _______________ a) Label the vertex: _______________

b) This graph opens up / down , b) This graph opens up / down ,

so 𝑎 must be positive / negative. so 𝑎 must be positive / negative.

c) Possible equation: _______________ c) Possible equation: ______________

d) Label the 𝑥-intercept(s): __________ d) Label the root(s): _______________

e) Label the 𝑦-intercept: ____________ e) Label the 𝑦-intercept: ___________

f) This graph rises / falls to the right. f) This graph rises / falls to the right.

g) This graph has a minimum / maximum g) This graph has a minimum / maximum

Name ___________________________________________________ Date __________________ Block __________

2.3 Assignment – Sketching Quadratic Equations

Fill in the table for each equation.

Equation Vertex Opens up or

down? Why?

Total

number of

roots

Sketch

𝑦 = (𝑥 + 1)2 + 1

𝑦 = (𝑥 + 2)2 − 3

𝑦 = −(𝑥 − 4)2

𝑦 = −(𝑥 + 3)2 + 4

𝑦 = 𝑥 2 + 4

Equation Vertex Opens up or

down? Why?

Total

Number of

Roots

Sketch

(3, 0) 𝑎 is positive

(0, −5) down

(−2, 4) 𝑎 is negative

(1, −2)

2

(−2, −2)

0

Name ________________________________________________ Date ____________________ Block __________

2.4 Assignment – Solving Quadratic Equations

Perform the indicated operation.

1. (𝑥2 + 2𝑥 − 3) + (5𝑥3 − 4𝑥2 + 3) 2. (2𝑥 + 3)2

Use the Square Root Method to solve the quadratic equations.

3. 2𝑥2 − 8 = 0 4. 𝑥2 + 1 = 10

5. 𝑥2 − 16 = 0 6. 4𝑥2 = 100

7. −(𝑥 − 5)2 + 18 = 2 8. (𝑥 + 3)2 − 1 = 99

Find the 𝒙-intercepts and use the vertex to sketch the following equations. Label your points on the graph.

9. (𝑥 − 3)2 − 16 = 0 10. 3(𝑥 + 2)2 − 27 = 0

a) Vertex: _______ a) Vertex: _______

b) The graph opens up / down b) The graph opens up / down

because 𝑎 is positive / negative because 𝑎 is positive / negative

c) 𝑥-intercept(s): _______ c) 𝑥-intercept(s): _______

d) Real roots: _______ d) Real roots: _______

e) The vertex is a minimum / maximum e) The vertex is a minimum / maximum

Name _____________________________________________________ Date ___________________ Block _______

FUNCTION FAMILIES

Solve the following equations. Make certain you know WHAT KIND of equation you’re solving.

1. 5(−3 + 𝑥) = 20 2. |2𝑥 − 3| − 4 = 3 3. −(𝑥 − 5)2 + 18 = 2

4. (𝑥 − 3)2 − 12 = 4 5. −3(𝑥 − 8) = −36 6. 2|𝑥 + 4| = 18

7. 6(5𝑥 + 6) − 5 = 1 8. −10|4𝑥 − 2| + 6 = −54 9. 𝑥2 + 1 = 10

10. |𝑥 − 63| + 5 = 3 11. 3(𝑥 + 2)2 − 27 = 0 12. −6𝑥 − 3(𝑥 + 20) = −15

Graph the following equations. Make certain you know WHAT KIND of equation you’re graphing. Label your points.

1. 𝑦 = (𝑥 + 2)2 − 3 2. 𝑦 =1

2𝑥 − 5

3. 𝑦 =3

2|𝑥 − 1| 4. 𝑦 = −2(𝑥 + 3)2 + 4

5. 𝑦 = −2|𝑥 − 1| + 3 6. 𝑦 = −3𝑥 + 4

Name _________________________________________________ Date _______________ Block __________

AFDA Unit 2 Test Review

Perform the indicated operation.

1. (−2𝑥2 + 3𝑥 − 1) + (3𝑥3 − 4𝑥 + 6) 2. (3𝑥 − 1)(𝑥2 + 3𝑥 − 4)

3. (4𝑥2 − 7𝑥 + 2) − (3𝑥3 + 2𝑥2 − 5𝑥) 4. (2𝑥 − 5)2

Answer the questions and write the equation for the following graphs. Use the form 𝒚 = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌.

5. Vertex: _______ 6. Vertex: _______

𝑎 is ________________ 𝑎 is _______________

# of Real Roots: _______ # of Real Roots: _____

Possible Equation: Possible Equation:

____________________ __________________

Minimum / Maximum Minimum / Maximum

7. Vertex: _______ 8. Vertex: _______

𝑎 is _________________ 𝑎 is _______________

# of Real Roots: _______ # of Real Roots: _____

Possible Equation: Possible Equation:

____________________ __________________

Minimum / Maximum Minimum / Maximum

Solve the following quadratic equations using the Square Root Method.

9. −2𝑥2 + 18 = 0 10. 3(𝑥 − 1)2 − 4 = 8

Answer the questions for each quadratic equation, then graph.

11. 𝑦 = (𝑥 − 1)2 − 9 12. 𝑦 = −2(𝑥 + 3)2 + 8

a) Vertex: _______ a) Vertex: _______

b) The graph opens up / down b) The graph opens up / down

c) Find the 𝑥-intercepts by solving the equation. c) Find the 𝑥-intercepts by solving the equation.

________________________________________ ________________________________________

d) Plot the vertex and the 𝑥-intercepts. Don’t forget d) Plot the vertex and the 𝑥-intercepts. Don’t forget

to label them. Draw your graph using these points. to label them. Draw your graph using these points.