Review for Midterm #2

REVIEW FOR MIDTERM #2

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.

____ 1.

a. / linear function
linear term:
constant term: 6 / c. / linear function
linear term:
constant term: –6
b. / quadratic function
quadratic term:
linear term:
constant term: 6 / d. / quadratic function
quadratic term:
linear term:
constant term: –6

____ 2.

a. / linear function
linear term:
constant term: –6 / c. / quadratic function
quadratic term:
linear term:
constant term: –6
b. / quadratic function
quadratic term:
linear term:
constant term: –6 / d. / linear function
linear term:
constant term: –6

Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.

____ 3.

a. / (–1, –2), x = –1
P'(0, –1), Q'(–3, 2) / c. / (–1, –2), x = –1
P'(–2, –1), Q'(–1, 2)
b. / (–2, –1), x = –2
P'(–2, –1), Q'(–1, 2) / d. / (–2, –1), x = –2
P'(0, –1), Q'(–3, 2)

____ 4.

a. / (–3, 1), x = –3;
P'(–2, 0), Q'(–5, –3) / c. / (–3, 1), x = –3;
P'(–4, 0), Q'(–1, –3)
b. / (1, –3), x = 1;
P'(–2, 0), Q'(–5, –3) / d. / (1, –3), x = 1;
P'(–4, 0), Q'(–1, –3)

____ 5. Find a quadratic function to model the values in the table. Predict the value of y for x=6.

x / y
–1 / 2
0 / –2
3 / 10
a. / ; –58 / c. / ; 58
b. / ; 60 / d. / ; –58

Find a quadratic model for the set of values.

____ 6. (–2, 8), (0, –4), (4, 68)

a. / / c. /
b. / / d. /

____ 7.

x / –2 / 0 / 4
f(x) / 1 / –3 / 85
a. / / c. /
b. / / d. /

____ 8. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake’s population of waterfowl on each of the next six weeks.

Week / 0 / 1 / 2 / 3 / 4 / 5 / 6
Population / 585 / 582 / 629 / 726 / 873 / 1,070 / 1,317
a. / Find a quadratic function that models the data as a function of x, the number of weeks.
b. / Use the model to estimate the number of waterfowl at the lake on week 8.
a. / ; 1,614 waterfowl
b. / ; 2,679 waterfowl
c. / ; 1,961 waterfowl
d. / ; 2,201 waterfowl

____ 9. A manufacturer determines that the number of drills it can sell is given by the formula , where p is the price of the drills in dollars.

a. / At what price will the manufacturer sell the maximum number of drills?
b. / What is the maximum number of drills that can be sold?
a. / $60; 285 drills / c. / $31; 2,418 drills
b. / $30; 2,415 drills / d. / $90; 8,385 drills

____ 10. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula , where x is the number of units produced per week, in thousands.

a. / How many units should the company produce per week to earn the maximum profit?
b. / Find the maximum weekly profit.
a. / 1,000 units; $1300 / c. / 1,000 units; $600
b. / 3,000 units; $100 / d. / 2,000 units; $1100

____ 11. Which is the graph of ?

a. / / c. /
b. / / d. /

____ 12. Use vertex form to write the equation of the parabola.

a. / / c. /
b. / / d. /

____ 13. Identify the vertex and the y-intercept of the graph of the function .

a. / vertex: (–2, 5);
y-intercept: –7 / c. / vertex: (2, 5);
y-intercept: –7
b. / vertex: (2, –5);
y-intercept: –12 / d. / vertex: (–2, –5);
y-intercept: 9

____ 14. Write in vertex form.

a. / / c. /
b. / / d. /

Write the equation of the parabola in vertex form.

____ 15. vertex (–4, 3), point (4, 131)

a. / / c. /
b. / / d. /

____ 16. vertex (0, 3), point (–4, –45)

a. / / c. /
b. / / d. /

Factor the expression.

____ 17.

a. / / c. /
b. / / d. /

____ 18.

a. / / c. /
b. / / d. /

____ 19.

a. / / c. /
b. / / d. /

____ 20.

a. / / c. /
b. / / d. /

____ 21.

a. / / c. /
b. / / d. /

____ 22.

a. / / c. /
b. / / d. /

____ 23.

a. / / c. /
b. / / d. /

____ 24.

a. / / c. /
b. / / d. /

____ 25.

a. / / c. /
b. / / d. /

____ 26.

a. / / c. /
b. / / d. /

____ 27.

a. / / c. /
b. / / d. /

____ 28.

a. / / c. /
b. / / d. / no solution

____ 29. Solve by factoring.

= 0

a. / 8, / b. / –8, 4 / c. / –8, / d. / ,

Solve the equation by finding square roots.

____ 30.

a. / / c. /
b. / , – / d. /

____ 31.

a. / , / b. / , / c. / , / d. / ,

____ 32. The function models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.

a. / 7.79 seconds / c. / 0.25 seconds
b. / 11.02 seconds / d. / 5.51 seconds

____ 33. Use a graphing calculator to solve the equation . If necessary, round to the nearest hundredth.

a. / 1.16, –1.16 / c. / 2.95, –1.7
b. / 1.47, –0.85 / d. / 0.85, –1.47

____ 34. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard.

a. / 17.1 yards / c. / 39.2 yards
b. / 34.2 yards / d. / 152.6 yards

____ 35. Simplify using the imaginary number i.

a. / / b. / / c. / / d. /

Write the number in the form a + bi.

____ 36.

a. / / c. /
b. / / d. /

____ 37. –6 –

a. / / c. /
b. / / d. /

____ 38. Find .

a. / –9 / b. / 9 / c. / / d. /

____ 39. Identify the graph of the complex number .

a. / / c. /
b. / / d. /

____ 40. Find the additive inverse of .

a. / / c. /
b. / / d. /

Simplify the expression.

____ 41.

a. / / c. /
b. / / d. /

____ 42.

a. / / c. /
b. / / d. /

____ 43.

a. / 36 / b. / –36 / c. / –36i / d. / 36i

____ 44.

a. / / c. /
b. / / d. /

Solve the equation.

____ 45.

a. / i, i / c. / i, i
b. / i, i / d. / ,

____ 46.

a. / 14 / b. / –8 / c. / 4 / d. / –6

____ 47.

a. / 1 / b. / –7 / c. / –1 / d. / –1

____ 48.

a. / –5, 11 / b. / 5 / c. / 11 / d. / –11

____ 49. Find the first three output values of the fractal-generating function . Use z=0 as the first input value.

a. / , 536828 + 336604i
b. / , 536828 + 336604i
c. /
d. / , 536828 + 336604i

____ 50. Two complex numbers a + bi and c + di are equal when a = c and b = d. Solve the equation for x and y, where x and y are real numbers.

a. / x = ; y = / c. / x = ; y =
b. / x = ; y = / d. / x = ; y =

Use the Quadratic Formula to solve the equation.

____ 51.

a. / , / b. / , / c. / , / d. / ,

____ 52.

a. / / c. /
b. / / d. /

____ 53.

a. / / c. /
b. / / d. /

____ 54. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation . Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

a. / 12.7 yards / c. / 10.2 yards
b. / 20.4 yards / d. / 320 yards

____ 55. Classify –3x5 – 2x3 by degree and by number of terms.

a. / quintic binomial / c. / quintic trinomial
b. / quartic binomial / d. / quartic trinomial

____ 56. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.

a. / quartic trinomial / c. / cubic binomial
b. / quintic trinomial / d. / quadratic binomial

____ 57. Zach wrote the formula w(w – 1)(5w + 4) for the volume of a rectangular prism he is designing, with width w, which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number of terms.

a. / ; quintic trinomial
b. / ; quadratic monomial
c. / ; cubic trinomial
d. / ; quartic trinomial

____ 58. Write the polynomial in standard form.

a. / / c. /
b. / / d. /

____ 59. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.

a. / 2x + 9x4; quintic binomial / c. / 2x5 – 8x4; quintic trinomial
b. / 20x5 – 8x4; quintic binomial / d. / 20x5 – 10x4; quartic binomial

____ 60. Use a graphing calculator to determine which type of model best fits the values in the table.

x / –6 / –2 / 0 / 2 / 6
y / –6 / –2 / 0 / 2 / 6
a. / quadratic model / c. / linear model
b. / cubic model / d. / none of these

____ 61. Use a graphing calculator to find a polynomial function to model the data.

x / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
f(x) / 12 / 4 / 5 / 13 / 9 / 16 / 19 / 16 / 24 / 43
a. / f(x) = 0.8x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58
b. / f(x) = 0.08x3 – 1.73x2 + 12.67x + 35.58
c. / f(x) = 0.08x4 + 1.73x3 – 12.67x2 + 34.68x – 35.58
d. / f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58

____ 62. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1995. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 2006.

Years since 1995 / 1 / 3 / 5 / 7 / 9
Trees planted (in thousands) / 1.3 / 18.3 / 70.5 / 177.1 / 357.3
a. / ; 630.3 thousand trees
b. / ; 630.3 thousand trees
c. / ; 618.1 thousand trees
d. / ; 618.1 thousand trees

____ 63. The table shows the number of llamas born on llama ranches worldwide since 1988. Find a cubic function to model the data and use it to estimate the number of births in 1999.

Years since 1988 / 1 / 3 / 5 / 7 / 9
Llamas born (in thousands) / 1.6 / 20 / 79.2 / 203.2 / 416
a. / ; 741,600 llamas
b. / ; 563,200 llamas
c. / ; 741,600 llamas
d. / ; 563,200 llamas

____ 64. Write the expression (x + 6)(x – 4) as a polynomial in standard form.

a. / x2 – 10x + 2 / c. / x2 + 2x – 24
b. / x2 + 10x – 24 / d. / x2 + 10x – 10

____ 65. Write 4x3 + 8x2 – 96x in factored form.

a. / 6x(x + 4)(x – 4) / c. / 4x(x + 6)(x + 4)
b. / 4x(x – 4)(x + 6) / d. / –4x(x + 6)(x + 4)

____ 66. Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a volume defined by the function . Graph the function. What is the maximum volume for the domain ? Round to the nearest cubic foot.