REVIEW GUIDE FOR UNIT 2 TEST ON 11/25
TOPICS:
Graph linear equations using knowledge of slope intercept form
Graph absolute value and quadratic functions using knowledge of vertex form
Graph quadratic functions by finding axis of symmetry and creating a table of values
Given a quadratic function, determine domain, range, and if vertex is a max or min point
Determine the x/y intercepts of linear and absolute value functions graphically and algebraically
Graph linear, absolute value, and quadratic inequalities
Solve systems of linear equations using graphing, substitution, and elimination method
Solve word problems by creating a system of equations and using the method of your choice
Solve systems of linear, absolute value, and quadratic equations using graphing method
Solve systems of linear, absolute value, and quadratic inequalities using graphing method
Part 1: Put each linear equation or inequality in slope intercept form
1.
3x +5y =20
2.
-4x - y = -7
3.
Part 2: Graph each function on the coordinate plane provided
4.
y = 3x - 6
5.
2
y =- x+4
5
-2y - x ≤ 6
6.
f(x) = - x - 6 + 4
8.
f(x) = ( x -3) -5
2
7.
f(x) = 3 x - 7
9.
f(x) = - ( x + 6)
2
Part 3: Graph the quadratic function below by finding the axis of symmetry and creating a table of values
10.
a=
f(x) =2x2 - 8x +1
b=
a) Use x =
-b
to find the axis of symmetry
2a
c=
b) Create a table of values
c) Is the vertex a
max or min?
d) Find the domain
e) Find the range
Part 4: Determine the x and y-intercept for each function
11.
13a.
f ( x) = x +3 - 8
12.
f ( x) = x +5 + 8
1
y = x-8
2
13b. Now graph f ( x) = x +5 + 8
to see if your answer to 13a makes sense
Part 5: Graph each inequality on the coordinate plane provided
14.
3
f(x) ≤ x + 8
2
15.
f(x) >
1
x-5
4
16.
2
f(x) < - ( x - 6) + 4
Part 6: Solve each system of equations using the indicated method
17. Graphing Method
1
y = x-4
2
x=4
y = -2x + 6
19. Substitution Method
18. Graphing Method
1
y = x+7
2
1
y = x-4
2
20. Substitution Method
y = 3x - 4
x -2y = 3
2x - 3y = -2
4x - 8y = 12
21. Elimination Method
22. Elimination Method
3x +2y = 12
7x +2y = 6
6x - 5y = -3
3x - 5y =26
Part 7: For each word problem, define your variables, create a system of equations, and solve
23. Mike’s school is selling tickets to the choral concert. On the first day of ticket sales, the school sold
30 senior citizen tickets and 25 regular tickets for a total of $160. The school took in $190 on the
second day by selling 15 senior citizen tickets and 40 regular tickets. What is the cost of each type of
ticket?
24. An English quiz contains multiple choice and essay questions. Multiple-choice questions are worth
2 points each and essay questions are worth 10 points each. The quiz has a total of 18 questions
and is worth 60 points. How many of each type of question appears on the quiz?
25. Rob has 23 coins in his piggy bank worth a total of $4.55. He only h as quarters and nickels. How
many of each type of coin does Rob have?
Part 8: Solve each system using the graphing method
f(x) = ( x + 3)
26.
2
x = -5
2
x +5
3
2
f(x) = x + 1
3
f(x) = -
27.
f(x) = - x + 3 + 6
Part 9: Solve each system of inequalities using the graphing method
28.
1
y > - x +1
4
2
y ≤ x-3
3
y < 2x - 3
29.
1
y ≤- x+4
5
x ≤3
30.
f(x) > x - 4 -2
2
f(x) £ - ( x + 3) + 9
f(x) >
31.
1
x +2
4
2
f(x) ≥ ( x - 6) - 1
f(x) < 7