Download Algebra 2 Accelerated

Algebra 2 Accelerated
Chapter 6 Practice Test
104 Total Points
1. Find a cubic model for the following function. Then use your model to estimate the value of y when
x = 7. Round to two decimal places where necessary. (4 points)
x
y
y = -.06x3+.98x2-4.93x+28.36
0
25
2
21
4
20
6
23
8
19
10
17
y = 21.29 when x = 7
2. Write each polynomial in standard form. Then classify it by degree and number of terms. (4 points
each)
a.
x 2  x 4  2x 2
c.
-x4+3x2
quartic binomial
c
hc
b. 3 2c 2  9  3c 2  7
b gb g
x 2x 4x  1
8x3+2x2
cubic binomial
h
d.
3x2+16
quadratic binomial
ba  bgba  bg
2
a3-a2b-ab2+b3
cubic 4 terms
3. For each function, determine the zeros. State the multiplicity of any multiple zeros. (4 points each)
a.
b g
y  x x 8
0
8 mult. 2
2
b gb g
b. y  2 x  5 x  3
-5/2
3 mult. 2
2
c.
f ( x)  x 4  8x 3  16x 2
0 mult. 2
4 mult. 2
4. A rectangular box is 2x + 3 units long, 2x – 3 units wide, and 3x units high. Express its volume as a
polynomial in standard form. (4 points)
12x3 – 27x
5. Find the relative minimum, relative maximum and zeros of the following function. (4 points)
a.
f ( x)   x 3  16 x 2  76 x  96
min = -16.9
max = 5.05
zeros = 2, 6, 8
6. Write a polynomial function in standard form with the given zeros. (4 points each)
a.
x  1,1,2
b. x  2,0,1
x3 + 2x2 – x – 2
x3 + x2 – 2x
7. Divide using synthetic division. (3 points each)
a.
cx  7 x
3
2
hb g
 7 x  20  x  4
x2 – 11x + 37 R -128
b.
c6x
2
hb g
 8x  2  x  1
6x – 2 R -4
8. Solve each equation by graphing. Where necessary, round to the nearest hundredth. (3 points each)
a. 2 x 4  9 x 2  4
x = ±2, ±.71
b. 4 x 3  4 x 2  3x
x = -.5, 0, 1.5
9. Solve each equation by factoring. You must show work for credit. (4 points each)
a.
x 3  27  0
x = -3
x=
3
 2i 2
2
c.
x 4  10x 2  9  0
x = ±1, ±3
d. x 4  3x 2  4  0
b. 8 x 3  1  0
x=½ x=
1 i 3

4
4
x = ±1 x = ±2i
10. Find the roots of each polynomial equation. You must show work for credit. (4 points each)
a. 2 x 3  13x 2  17 x  12  0
-3, -4, .5
b. x 3  8x 2  200  0
10,  1  i 19
11. Find a polynomial equation with rational coefficients that has the given numbers as roots. (5 points
each)
a. 3  i and  3
x3 – 3x2 – 8x + 30
b.
3 and 1  i
x4 – 2x3 – x2 + 6x - 6
12. Use Pascal’s Triangle to expand each binomial. (5 points each)
a.
bx  4g
6
a. x6 + 24x5 + 240x4 + 1280x3 + 3840x2 + 6144x + 4096
b. 16n4 + 64n3 + 96n2 + 64n + 16
b.
b2n  2g
4