Precalculus Honors - Chapter 1 and 2 Test REVIEW
... What is the degree of the polynomial?
2. A polynomial P(x) = anxn + an^ixn~-( + —h a0 has at most how many roots?
3. Solve 2x 3 - 8x2 + 3x - 12 = 0.
4. Solve x6 - x 4 + I6x2 -16 = 0.
5. Sketch /(x) = x + x3 — x2 — x. Use a sign chart and show all work.
.
6. Sketch f(x) — x3 — 6x2 + 9x. Use a sign chart and show all work.
7. Is x 4 + 3x3 - 2x + 9 divisible by x - 1?
8. Divide using long division:
2x5+4x3-2x2+l
x2-3
9. Find the number n such that the equation
/(%) = x5 + 5x 4 — nx3 + 2x2 - 1 has a root of x = 2.
10. What are the possible roots of y = -6x 4 - 3x + 2?
11. Use the Rational Root Theorem to find all real roots
of/(x) = x 3 + 2x2 -x-2.
12. Write an equation whose roots are -3,4, 5 + i.
13-Simplify:
4
2 + 7i
1
3i
9-i
For each function, identify all vertical, horizontal and slant asymptotes (if any), find the zeros and graph.
£,
I4.f(x)
x
4x2
Cf
= —2
x -3
N
lS.f(x)
x3+2x-4
x2-9
•
V.A. =
H.A.
=
V.A. =
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;
. ;
H.A. =
S.A. =
S.A. =
Zeros =
Zeros =
Write the quadratic in vertex form and sketch the graph.
16. y = 2x2 -I2x + 13
17. y = -x2 + 4x + 14
3
^
•
18. The path of a projectile is: h(x~) =
12 + 3t + 5 where h is the height of the projectile and t is the time after the
projectile is launched. Find the maximum height of the projectile and how far away it is from its original location when it
lands. At what time does the projectile reach a height of 20 feet?
Precalculus Honors - Chapter 1 and 2 Test REVIEW
A/hat is the degree of the polynomial?
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pou^r
o<
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'
2. A polynomial P(x) = anxn + an_1xn~i + —I- a0 has at most how many roots?
3. Solve 2x3 - 8x2 + 3x - 12 = 0.
4. Solve x 6 - z 4 + 16x2 -16 = 0
5. Sketch f(x) = x* + x3 - x2 - x. Use a sign chart and show all work.
o=
- -f- -
^/
X-
*2.
X ~ 2.
3
2
-*-
+
6. Sketch /(*) = x - 6x + 9x; Use a sign chart and show all work.
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CP
3
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o
-
- - =
7. Is x 4 + 3x3 -2x + 9 divisible by x - 1?
I
f-
3
o
I
V
•
-
8. Divide using long division:
2x5+4x3-2x2+:
X2-3
9. Find the number n such that the equation
/O) = x 5 + 5x 4 - nz3 + 2x2 - 1 has a root of x = 2.
lox3 to **-
-i
-2.
10. What are the possible roots of y = -6x 4 - 3z + 2?
11. Use the Rational Root Theorem to find all real roots
of/(x) = x 3 + 2x2 -x-2.
-z
7.
(
0
/> fyi, l i .
12. Write an equation whose roots are —3,4,5 + i.
IS.Simplify:
-/
4
2+7l
1
3i
9-1
For each function, identify sll vertical, horizontal and slant asymptotes (if am/}, find the zeros and graph.
/
/"
"\
f Oy* i
i Si I
V
-^
——
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TTifti
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s
O
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Zeros =
Write the quadratic in vertex form and sketch the graph.
16. y = 2x 2 -12x + 13
17.y = i;
t f .
18. The path of a projectile is: /i(x) = — — t2 + 3t + 5 where h is the height of the projectile and t is the time after the
projectile is launched. Find the maximum height of the projectile and how far away it is from its original location when it
lands. At what time does the projectile reach a height of 20 feet?