Transcript Advanced Algebra II Chapter 7 Review Sheet
Advanced Algebra II Chapter 7 Review Sheet
1. Identify the degree of each polynomial: a)
0 .
2
x
1 .
5
x
2 3 .
2
x
3
b)
5
x
2 6
x
5 2
x
6 3
x
4 8
2. Determine which of the expressions are polynomials: a) 25 b)
x
1
x
2
c)
x
3
x
2 5
d)
1
x
2 .
3
x
3. The figures below represent the triangular numbers. a) Complete the table:
N
Nth #
1
1
2
3
3
6
4
10
5
15
6
21
7
28 b) Calculate the finite differences for the completed table. Second differences are all one.
c) What is the degree of the polynomial function that you would use to model this data set?
2 nd degree:
y
ax
2
bx
c
d) Write a polynomial function t that gives the nth triangular number as a function of n.
y
1 2
x
2 1 2
x
4. Tell whether each equation is written in general form, vertex form, or factored form. Then write each equation in the other two forms.
a)
vertex y
2 (
x
2 3 ) 2 1 4
general factored
: :
y y
2
x
2 2 (
x
8 3
x
23 36 .
313 )(
x
1 .
02 ) b)
y
2 (
x
8 )(
x
6 )
factored
:
general
:
y
2
x
2 4
x
96
vertex
:
y
2 (
x
1 ) 2 98 c)
y
3
x
2 4
x
5
general vertex
:
y
3 (
x
2 3 ) 2 11 3
factored
:
y
(
x
( 2 3 11
i
))(
x
3 ( 2 3 11
i
)) 3 5. Solve each equation: a) (
x
7 )(
x
3 ) 5 2
x a
) 3
b
) 0 , 7 , 3 35 b)
x
3 10
x
2 21
x
6. Write the equation of each graph in factored form:
a
)
y
(
x
1 )(
x
3 )
b
)
y
1 .
8 (
x
2 .
4 )(
x
.
8 )
c
)
y
1 2 (
x
2 )(
x
3 )
6. A ball is thrown up and off the roof of a 75 m tall building with an initial velocity of 14.7 m/s.
a) Let t represent the time in seconds and h represent the height of the ball in meters. Write an equation that models the height of the ball.
y
4 .
9
x
2 14 .
7
x
75 b) At what time does the ball reach maximum height? What is the ball’s maximum height?
1.5 seconds c) At what time or times is the ball 30 m above the ground?
4.88 seconds d) At what time does the ball hit the ground?
5.69 seconds
Factor each expression over
real
numbers:
a
)
uv
5
u
v
2 5
v b
)
ad
3
a
d
2 3
d c
) 54
x
2 24
d
) 10
x
2 17
x
3
e
) 125
x
3 1
f
)
x
6
y
6
a
)(
u
v
)(
v
5 )
b
)(
a
d
)(
d
3 )
c
) 6 ( 3
x
2 )( 3
x
2 )
d
)( 5
x
1 )( 2
x
3 )
e
)( 5
x
1 )( 25
x
2 5
x
1 )
f
)(
x
y
)(
x
2
xy
y
2 )(
x
y
)(
x
2
xy
y
2 )
8. Perform each operation on complex numbers: a) ( -4 + 3i) – (4 – 2i) b) (6 – 8i) + (9 +3i) c) (-2 + 8i)(-3 – 3i) d) 7 3
i
4 2
i
a) – 8 + 5i b) 15 – 5i c) 30 – 18i
d
11 13
i
) 10 1 .
1 1 .
3
i
9) Write the function in vertex form and state the vertex:
y
3
x
2 15
x
2
y
3 (
x
5 2 ) 2 83 4 10) Solve:
a
)
x
2 3
x
10 0
b
) 4
x
2 7
x
1
c
)
x
2 5 .
8
x d
)
x
2 5
x
24 0
e
)
x
(
x
5 ) 1
f
)
x
2 2
x
5 0
a
) 5 , 2
b
) 7 8
c
) 0 , 5 .
8
d
) 8 , 3 5
e
)
f
2 ) 1 2
i
29 65
11) Find the zeros of the given functions:
a
)
y
2 (
x
2 )(
x
1 )
b
)
y
x
2 6
x
25 a) 2, -1 b) 3+/- 4i