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The graph of the equation is shown below.
What is y = (x +
2
1) ?
The equation of the
parabola with this vertex is
f(x) = (x + 8)2 - 4
The function for this
graph is
f(x) = (x –
2
5)
– 1.
What is
This quadratic equation
has a maximum point at
(3, -4).
What is
f(x) = (x –
2
3)
– 4?
The cost in millions of dollars for
a company to manufacture x
thousand automobiles is given by
the function
C(x) = 3x2 – 18x + 63. Find the
number of automobiles that must
be produced to minimize the cost.
3 thousand automobiles
Determine if the
following is a
polynomial function. If
so, give the degree.
f(x) = x2 – 3x7
Use the leading coefficient
test to determine the end
behavior for
f(x) = 6x3 + 3x2 – 3x - 1
Up to the right,
Down to the left.
Find the zeros and their
multiplicities of the
function.
F(x) = 4(x + 5)(x – 1)2
-1, multiplicity 1
1, multiplicity 2
Graph the function.
F(x) = x2(x – 3)(x – 2)
Use synthetic division to
divide.
3x2 + 29x + 56
x+7
3x + 8
Divide using synthetic
division.
x  x 5
x2
5
3
4
x +
3
2x
R. 45
+
2
5x
+ 10x + 20.
Find f(-3) given
f(x) = 4x3 – 6x2 – 5x + 6
Solve the equation
3x3 – 28x2 + 51x – 14 = 0
given that 2 is one solution.
2, 7, 1/3
Use synthetic division to
find all zeros of
f(x) =
3
x
–
2
3x
– 18x + 40.
Use the rational zeros theorem
to list all possible rational zeros
of f(x) = x5 – 3x2 + 6x + 14
 1,  2,  7,  14
Use the rational zeros
theorem to list all possible
rational zeros of
f(x) =
3
3x
–
2
17x
+ 18x + 8
and then use this root to find
all zeros of the function.
-1/3, 2, 4
Use Descartes’ Rule of Signs
to determine the possible
number of positive real
zeros and negative real
6
zeros for f(x) = x – 8.
1 positive real zero
1 negative real zero
Give all the roots of
f(x) =
3
x
+
2
5x
+ 12x – 18
1, -3 + 3i, - 3 – 3i
Use the graphing calculator to
determine the zeros of
f(x) =
3
x
–
2
6x
–x+6
1, 3, 4, or 5
1, -1, 6
Use the Upper Bound Theorem
to determine which of the
following is a good upper
bound for
f(x) =
4
x
+
3
x
–
1, 3, 4, or 5
2
7x
– 5x + 10
Find all roots of the
equation.
Hint: -2i is one root.
x4 – 21x2 – 100 = 0
Write the polynomial
function as a product of
linear factors.
f(x) =
4
x
–
2
3x
–4
f(x)= (x – 2)(x + 2)(x – i)(x + i)
Factor completely.
f(x) =
3
x
+
2
4x
–x-4
f(x)= (x – 1)(x + 1)(x + 4)
Give an equation for the
polynomial function that
has zeros of 2, -2, and 3
and has a degree of 3.
f(x)= (x – 2)(x + 2)(x – 3)
Other answers are possible.
Solve the inequality
and give your solution
in interval notation.
(x – 3)(x + 2) > 0
(-∞, -2) or (3, ∞)
Solve the inequality
and give your solution
in interval notation.
x2 + 3x – 18 > 0
(-∞, -6) or (3, ∞)
Solve the inequality
and give your solution
in interval notation.
x2 – 2x – 24 < 0
(-4, 6)
Solve the inequality
and give your solution
in interval notation.
x2 – 3x – 10 < 0
[-2, 5]
Solve the inequality
and give your solution
in interval notation.
x2 + 6x < – 8
[-4, -2]
-10 < x < 10
-10 < y < 60
y = (x – 2)2(x + 3)2