Download (x) = -2 x 2 +

Graph each polynomial function on a calculator. Describe the graph, and identify
the number of real zeros.
32. f (x) = -2x 2 + x - 1
33. g(x) = x 3 + 1
34. h(x) = x 4 - 6x 2 + 10
35. p(x) = -x 5 + x - 1
Complete the table.
Polynomial
Standard Form
Leading
Coefficient
Degree
2
36.
8x + 3x - 5
37.
3x 2 + x 4 - 2
38.
x3 - x4 + x - 1
39.
64 + x 2
40. Critical Thinking Write a quartic trinomial with a leading coefficient of 2.
Geometry Find a polynomial expression in terms of x for the surface area of
each figure.
41.
x
42.
43.
x+1
x+4
__1 x + 1
2
44.
3x
2x + 3
x
x
x-1
x-1
45. Business The manager of a gift-basket business will ship the baskets anywhere in
the country. The cost to mail a basket based on its weight x, in pounds, is given by
C(x) = 0.03x 3 - 0.75x 2 + 4.5x + 7.
a. What is the cost of shipping a 7-pound gift basket?
b. What is the cost of shipping a 19-pound gift basket?
46. Estimation Estimate the value of P(x) = -2.03x 3 + πx 2 - x + 5.8 for P(-2.78).
Tell whether each statement is sometimes, always, or never true. If it is sometimes
true, give examples to support your answer.
47. A quadratic polynomial is a trinomial.
48. The degree of a polynomial in standard form is equal to the degree of the first term.
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49. The leading coefficient of a polynomial is the greatest coefficient of any term.
50. The total number of lights in a triangular lighting rig is
related to the triangular numbers, as shown at right.
The nth triangular number is given by T (n) = __12 n 2 + __12 n.
a. Write a polynomial function that represents the
(n + 1)th triangular number, T (n + 1).
b. The difference between two consecutive triangular
numbers is T (n + 1) - T (n). Subtract these two
polynomial functions, and state a conclusion about the
difference between consecutive triangular numbers.
Triangular numbers:
1, 3, 6, 10, 15, . . .
3-1 Polynomials
155