Algebra 2
1.
1st Nine Weeks Review
How many solutions does the system of
equations have? What is the solution to the
system of equations?
DO ALL WORK ON YOUR OWN PAPER FOR CREDIT!
substitution
4.
2x  3y  8

x  5y  27
When solving the following system of
equations by elimination what will you
multiply the second equation by to eliminate
x? Justify your answer.
12x  3y  6

4x  5y  5
2.
Solve the system of equations by graphing.
(This is a multiple choice question justify
with math)
5.
Solve the systems of equations.
2 x  3 y  1

4 x  y  3
6.
Find the z-coordinate of the solution of the
system.
 2x  y  2z  7

  x  2y  4z  5
 x  4y  6z  1

7.
A worker finds a ball on the roof of a building
as he is doing some repairs. He tosses the ball
up and off the roof so that its height
 h in meters  above the ground is related to
x  y  2

2x  2y  8
a.
b.
time  t in seconds  after it has been tossed,
by the function h  t  4t   What was
the maximum height reached by the ball?
2
c.
8.
A manufacturer determines that the number of
drills it can sell is modeled by the equation
D  3p 2  180 p  285 , where p is the price of
drills in dollars. At what price will the
manufacturer sell the most number of drills?
What is the maximum number of drills that can
be sold?
9.
Write the equation of the parabola in vertex
form.
d.
3.
Solve the system of equations by
10.
How does the parabola open. Find the vertex
of the parabola, the maximum or minimum
11.
12.
13.
value, and the y-intercept.
y  3x 2  6x  5 .
24.
Solve by completing the square:
3 x 2  24 x  36  0
Use the graph of y = x² .If you translate the
parabola to the right 2 units and down 7
units, what is the equation of the new
parabola in vertex form?
25.
Solve using the quadratic formula.
5 x 2  15 x  30  0
26.
Solve: 5m 2  12  37
State how the parabola opens. State the
vertex and y-intercept:
2
f x   3x  1  5
27.
Simplify:
12 11i    8  3i 
28.
Simplify:
15  9i    24 17i 
29.
Simplify:
 8  2i  4  7i 
30.
Resort A charges $70 per night, plus a
one-time surcharge of $5. Resort B charges
$65 per night plus a one-time surcharge of
$20. After how many nights will the total
cost of the two options be the same?
a.
Define the variables
b.
Set up a system of equations to
solve the problem
c.
Solve system of equations
by substitution or elimination.
d.
What does the solution mean in
context of the word problem.
31.
The graph of which system of inequalities is
shown?
How does the parabola open? What is the
vertex and y-intercept of the graph
2
y  2  x  1  3 ?
14.
Solve the equation by factoring:
2x 2  13x  18  0
15.
Solve the equation by factoring:
2 x 2  2  3 x
16.
Solve the equation by factoring:
9x2  4  0
17.
18.
19.
Factor:
Factor:
Factor:
20.
Simplify:  x 2  2 x  5   2 x  3
21.
4
2
4
3
2
Simplify:  2 x  2 x    x  2 x  x  x  2 
22.
What value will complete the square?
18 x 2  2
3x 2  10x  8
x 2  11x  28
a. x  6 x  ___
2
2
x  ___
3
2
c. 2 x  5 x  ___
b. x 
2
23.
What number must be added to both sides of
the equation to complete the square?
x 2  6 x  ____  15  ____
a.
1
x
2
4 x  2y  8
c.
1
x
2
4 x  2y  8
y
y
b.
1
x
2
4 x  2y  8
d.
1
x
2
4 x  2y  8
y
y
32.
Given the Quadratic equation:
f  x   3x2  12x  7
a.
33.
34.
Does the graph of this function have
maximum or minimum?
Justify your answer
b.
Find the vertex algebraically.
c.
What is the y-intercept?
d.
Compare the width of the graph of
this function to the width of the
parent function. What causes this
change?
Two points on the parabolic path of a
catapulted smurf are (0,0) and vertex(24,12)
a.
Using vertex form, create an
equation that models the path of the
smurf
b.
At what coordinate (x, y) would the
smurf land?
c.
What does the y-coordinate of the
vertex represent?
Given f  x   x2  4 x  32
a.
Factor the function.
Write it in intercept form.
b.
What are the x-intercepts
c.
Using the x-intercepts.
What is the x-coordinate of
the vertex?
d.
What is the y-coordinate of
vertex