1.1 assignment solving multi-step equations€¦ · 1.1 assignment – solving multi-step equations...
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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.