Download Int Math 3 Review Handout (Sec.3-1 thru 3-7)

Name: __________________________________________
Int Math 3 Review Handout (Sec.3-1 thru 3-7)
2
Graph each function. How is each graph a translation of f(x) = x ?
1
2
y = (x + 3) + 4
A
C
f(x) translated down 4 unit(s) and
translated to the left 3 unit(s)
f(x) translated up 4 unit(s) and
translated to the right 3 unit(s)
B
D
f(x) translated up 4 unit(s) and
translated to the left 3 unit(s).
2
f(x) translated down 4 unit(s) and
translated to the right 3 unit(s)
2
Which expression is equivalent to −x + 8x + 75 = 13?
A
B
(x − 13)(x − 5) = 13
−(x − 13)(x + 5) = 3
−(x − 5)(x + 13) = 3
(x + 5)(x + 13) = 13
C
D
1
Name: ______________________
3
4
ID: A
2
Which is the graph of y = −2(x − 2) − 4?
A
C
B
D
Identify the vertex and the axis of
symmetry of the graph of the function
2
y = 2(x + 2) − 4.
A
B
C
D
What is the maximum or minimum
value of the function? What is the
range?
5
vertex: (–2, –4);
axis of symmetry: x = −2
vertex: (–2, 4);
axis of symmetry: x = −2
vertex: (2, 4);
axis of symmetry: x = 2
vertex: (2, –4);
axis of symmetry: x = 2
2
y = 2x + 28x − 8
A
B
C
D
2
minimum value: 7
range: y ≥ 7
minimum value: –106
range: y ≥ −106
minimum value: –7
range: y ≥ −7
minimum value: –106
range: y ≥ −7
Name: ______________________
6
7
Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1 and also
passes through the point (9, –1). Write the equation of the parabola in vertex form.
2
A
y = −2(x + 8) + 1
B
y = 2(x − 8) − 1
2
2
C
y = (x − 8) + 1
D
y = −2(x − 8) + 1
2
Identify the maximum or minimum
value and the domain and range of the
2
graph of the function y = 2(x + 2) − 3.
A
B
C
D
9
ID: A
8
minimum value: –3
domain: all real numbers
range: all real numbers ≥ −3
maximum value: –3
domain: all real numbers ≤ −3
range: all real numbers
minimum value: 3
domain: all real numbers ≥ 3
range: all real numbers
maximum value: 3
domain: all real numbers
range: all real numbers ≤ 3
Use the vertex form to write the
equation of the parabola.
2
A
y = 3(x + 2) + 2
B
y = 3(x − 2) + 2
C
y = 3(x − 2) − 2
D
y = (x + 2) + 2
2
2
2
You live near a bridge that goes over a river. The underneath side of the bridge is an arch
2
that can be modeled with the function y = −0.000495x + 0.619x where x and y are in feet. How
high above the river is the bridge (the top of the arch)? How long is the section of bridge
above the arch?
A
The bridge is about 193.52 ft above the river and the length of the bridge above
the arch is about 625.25 ft
B
The bridge is about 1250.51 ft above the river and the length of the bridge above
the arch is about 193.52 ft
C
The bridge is about 1250.51 ft above the river and the length of the bridge above
the arch is about 625.25 ft
D
The bridge is about 193.52 ft above the river and the length of the bridge above
the arch is about 1250.51 ft
3
Name: ______________________
ID: A
What is the graph of the equation?
2
10 y = −2x + 2x + 2
A
C
B
D
What is the number of real solutions?
2
11 8x − 11x = −3
A
B
no real solutions
two real solutions
one real solution
cannot be determined
C
D
4
Name: ______________________
ID: A
2
12 Compare the equation, y = 9x − 4x , the graph below, and the table below. Which has the
steepest rate of change from x = 1 to x = 2, and what is its value?
x
–1
1
2
3
A
graph, –1
B
equation, −
y
0
2
0
–4
1
3
1
2
C
table, −
D
equation, –3
What is the expression in factored form?
2
2
13 16x + 8x
A
B
C
D
14 −4x + 8x + 32
4x(4x + 2)
−4x(4x + 2)
4x(4x − 2)
4(4x + 2)
A
B
C
D
5
−4(x + 4)(x + 2)
−4(x − 4)(x + 2)
−4(x + 4)(x − 2)
−4(x − 4)(x − 2)
Name: ______________________
ID: A
Solve the equation.
2
15 x + 18x + 81 = 25
–14
–4, –14
A
B
14, 4
–4, 4
C
D
What are the solutions of the quadratic equation?
2
2
16 3x + 25x + 42 = 0
A –6, 3
1
B 6, −
2
7
1
C − , −
3 2
7
D –6, −
3
17 4x − 18x + 20 = 0
A 2, 4
5
B
,2
2
C –2, 2
5
D 2,
2
Solve by using tables. Give each answer to at most two decimal places.
2
2
18 −7x − 2 = −10x
A
B
C
D
19 The function h = −10t + 95 models the
path of a ball thrown by a boy where h
represents height, in feet, and t
represents the time, in seconds, that
the ball is in the air. Assuming the boy
lives at sea level where h = 0 ft, which is
a likely place the boy could have been
standing when he threw this ball?
–0.47, 0.47
0.24, 1.19
–1.19, –0.24
0.48, 2.38
A
B
C
D
What value completes the square for the expression?
2
20 x − 18x
A
B
81
−9
9
−81
C
D
6
a ladder
a bridge
an underground cave
his backyard
Name: ______________________
ID: A
Solve the quadratic equation by completing the square.
2
2
21 x + 10x + 14 = 0
C
−5 ± 11
5 ±6
−10 ± 6
D
100 ±
A
B
22 −3x + 7x = −5
11
67
A
7
±
3
B
−
7
±
3
109
C
−
7
±
6
22
D
7
±
6
3
3
6
109
6
Rewrite the equation in vertex form. Name the vertex and y-intercept.
23
2
y = x − 12x + 34
A
B
2
y = (x − 12) − 2
vertex: (–12, –2)
y-intercept: (0, –2)
2
y = (x − 6) − 2
vertex: (6, – 2)
y-intercept: (0, 34)
2
y = (x − 12) + 40
vertex: (–12, –2)
y-intercept: (0, –2)
2
y = (x − 6) + 70
vertex: (6, – 2)
y-intercept: (0, 34)
C
D
Use the Quadratic Formula to solve the equation.
2
2
24 −2x − 5x + 5 = 0
25 −4x + x = −4
32
A
−
5
±
4
B
−
5
±
4
C
−
4
±
5
130
D
−
5
±
2
65
2
65
4
4
2
7
A
1
±
8
B
8±
C
8±
D
1
±
4
65
8
130
8
65
8
65
4
Name: ______________________
ID: A
Use graphing to find the solutions to the system of equations.
26
ÔÏÔ
ÔÔ
ÔÔ y = x 2 + 7x + 7
ÌÔÔ
ÔÔ
ÔÔÓ
y= x + 2
A
C
(–5, 3)
(–1, –1)
B
(–4, –3)
(–2, –1)
D
(–4, 3)
(–2, 1)
(–5, –3)
(–1, 1)
8
Name: ______________________
ID: A
What is the solution of the quadratic system of equations?
27
ÔÏÔ
ÔÔ
ÔÔ y = x 2 + 18x + 35
ÔÌÔ
ÔÔÔ y = −x 2 + 2x + 5
ÔÓ
A
B
(–3, 98)
(–5, 150)
(–3, –10)
(–5, –30)
(–10, –3)
(–30, –5)
(3, –10)
(5, –30)
C
D
What is the solution of the system of inequalities?
28
ÔÏÔ
ÔÔ
ÔÔ y ≥ x 2 + 2x + 2
ÔÌÔ
ÔÔ
ÔÔ y < −x 2 − 4x − 2
Ó
A
C
B
D
9