1 Introduction To Algebraic Expressions 2 Equations, Inequalities, And Problem Solving 3 Introduction To Graphing 4 Polynomials 5 Polynomials And Factoring 6 Rational Expressions And Equations 7 Functions And Graphs 8 Systems Of Linear Equations And Problem Solving 9 Inequalities And Problem Solving 10 Exponents And Radicals 11 Quadratic Functions And Equations 12 Exponential Functions And Logarithmic Functions 13 Conic Sections 14 Sequences, Series, And The Binomial Theorem R Elementary Algebra Review A Mean, Median, And Mode B Sets C Synthetic Division And The Remainder Theorem expand_more
11.1 Quadratic Equations 11.2 The Quadratic Formula 11.3 Studying Solutions Of Quadratic Equations 11.4 Applications Involving Quadratic Equations 11.5 Equations Reducible To Quadratic 11.6 Quadratic Functions And Their Graphs 11.7 More About Graphing Quadratic Functions 11.8 Problem Solving And Quadratic Functions 11.9 Polynomial Inequalities And Rational Inequalities Chapter Questions expand_more
Problem 1YT: Solve 12x28x15 using the quadratic formula. Problem 2YT: For the quadratic function given by f(x)=2x22x3, find all x for which f(x)=0. Problem 3YT: 3. Solve: .
Problem 4YT: If f(x)=2+1x and g(x)=3z2, find all x for which f(x)=g(x). Problem 5YT Problem 1E: Solve Examine each exercise carefully, and solve using the easiest method. x23x10=0 Problem 2E: Solve Examine each exercise carefully, and solve using the easiest method. x2=121 Problem 3E: Solve. Examine each exercise carefully, and solve using the easiest method. x2+6x=10 Problem 4E: Solve. Examine each exercise carefully, and solve using the easiest method.
4.
Problem 5E: Solve. Examine each exercise carefully, and solve using the easiest method. (x+1)2=2 Problem 6E: Solve. Examine each exercise carefully, and solve using the easiest method. x210x+25=0 Problem 7E: Solve. Examine each exercise carefully, and solve using the easiest method. x22x=6 Problem 8E: Solve. Examine each exercise carefully, and solve using the easiest method. 4t2=11 Problem 1CYU Problem 2CYU Problem 3CYU Problem 4CYU Problem 1ES: Classify each of the following statements as either true or false. The quadratic formula can be used... Problem 2ES: Classify each of the following statements as either true or false. The steps used to derive the... Problem 3ES: Classify each of the following statements as either true or false. The quadratic formula does not... Problem 4ES: Classify each of the following statements as either true or false.
4. Solving by factoring is always... Problem 5ES: Classify each of the following statements as either true or false. A quadratic equation can have as... Problem 6ES: Classify each of the following statements as either true or false. It is possible for a quadratic... Problem 7ES: Solve. (Find all complex-number solutions.)
7.
Problem 8ES: Solve. (Find all complex-number solutions.) 3x27x+2=0 Problem 9ES: Solve. (Find all complex-number solutions.) u2+2u4=0 Problem 10ES: Solve. (Find all complex-number solutions.)
10.
Problem 11ES: Solve. (Find all complex-number solutions.)
11.
Problem 12ES: Solve. (Find all complex-number solutions.) t2+4t=1 Problem 13ES: Solve. (Find all complex-number solutions.) x2=3x+5 Problem 14ES: Solve. (Find all complex-number solutions.) x2+5x+3=0 Problem 15ES: Solve. (Find all complex-number solutions.) 3t(t+2)=1 Problem 16ES: Solve. (Find all complex-number solutions.) 2t(t+2)=1 Problem 17ES: Solve. (Find all complex-number solutions.)
17.
Problem 18ES: Solve. (Find all complex-number solutions.)
18.
Problem 19ES: Solve. (Find all complex-number solutions.)
19.
Problem 20ES: Solve. (Find all complex-number solutions.)
20.
Problem 21ES: Solve. (Find all complex-number solutions.)
21.
Problem 22ES: Solve. (Find all complex-number solutions.) p2+p+4=0 Problem 23ES: Solve. (Find all complex-number solutions.) x2+4x+6=0 Problem 24ES: Solve. (Find all complex-number solutions.)
24.
Problem 25ES: Solve. (Find all complex-number solutions.) 12t2+17t=40 Problem 26ES: Solve. (Find all complex-number solutions.) 15t2+7t=2 Problem 27ES: Solve. (Find all complex-number solutions.) 25x220x+4=0 Problem 28ES: Solve. (Find all complex-number solutions.)
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Problem 29ES: Solve. (Find all complex-number solutions.)
29.
Problem 30ES: Solve. (Find all complex-number solutions.)
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Problem 31ES: Solve. (Find all complex-number solutions.) 14(x4)(x+2)=(x+2)(x4) Problem 32ES: Solve. (Find all complex-number solutions.) 11(x2)+(x5)=(x+2)(x6) Problem 33ES: Solve. (Find all complex-number solutions.) 51p=2p2+72 Problem 34ES: Solve. (Find all complex-number solutions.)
34.
Problem 35ES: Solve. (Find all complex-number solutions.) x(x3)=x9 Problem 36ES: Solve. (Find all complex-number solutions.)
36.
Problem 37ES: Solve. (Find all complex-number solutions.)
37. (Hint: Factor the difference of cubes. Then the... Problem 38ES: Solve.(Find all complex-number solutions.) x3+1=0 Problem 39ES: Solve.(Find all complex-number solutions.)
39. Let Find x such that .
Problem 40ES: Solve.(Find all complex-number solutions.) Let g(x)=4x22x3. Find x such that g(x)=0. Problem 41ES: Solve. (Find all complex-number solutions.) Let f(x)=7x+7x+4 Find all x for which f(x)=1. Problem 42ES: Solve. (Find all complex-number solutions.)
42. Let
Find all x for which .
Problem 43ES: Solve. (Find all complex-number solutions.) Let F(x)=3x4andG(x)=14x Find all x for which F(x)=G(x). Problem 44ES: Solve. (Find all complex-number solutions.)
44. Let
.
Find all x for which .
Problem 45ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 46ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 47ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 48ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 49ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 50ES: Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places,... Problem 51ES: Solve using the quadratic formula Then use a calculator to approximate, to three decimal places, the... Problem 52ES: Solve using the quadratic formula Then use a calculator to approximate, to three decimal places, the... Problem 53ES: Simplify.
53.
Problem 54ES: Simplify. 1003/2[10.2] Problem 55ES: Simplify. x1/4x2/3[10.2] Problem 56ES: Simplify. (272)1/3[10.2] Problem 57ES: Simplify. 18a5bc1024a5bc3[4.2] Problem 58ES: Simplify. (2xw33x4w)2 [4.2] Problem 59ES: Synthesis Explain how you could use the quadratic formula to help factor a quadratic polynomial. Problem 60ES: Synthesis
60. If , then 2a is positive and the equivalent equation, , can be solved using the... Problem 61ES: For Exercises 61-63, let
and .
61. Find the x-intercepts of the graph of f.
Problem 62ES: For Exercises 61-63, let
and .
62. Find the x-intercepts of the graph of g.
Problem 63ES: For Exercises 61-63, let f(x)=x2x2+1 and g(x)=4x2x2+x+42. Find all x for which f(x)=g(x). Problem 64ES: Solve. Approximate the solutions to three decimal places.
64.
Problem 65ES: Solve. Approximate the solutions to three decimal places.
65.
Problem 66ES: Solve. (1+3)x2(3+23)x+3=0 Problem 67ES: Solve. 2x2+5x+2=0 Problem 68ES: Solve. ix22x+1=0 Problem 69ES: Solve.
69. One solution of . Find the other.
Problem 70ES: 70. Use a graphing calculator to solve Exercises 9, 27, and 43.
Problem 71ES: Use a graphing calculator to solve Exercises 11, 33, and 41. Use the method of graphing each side of... Problem 72ES: Can a graphing calculator be used to solve and quadratic equation? Why or why not? Problem 1QQ: 1. Solve using the principle of zero products:
[11.1]
Problem 2QQ: 2. Solve using the principle of square roots:
.
[11.1]
Problem 3QQ: 3. Solve by completing the square:
[11.1]
Problem 4QQ: Solve using the quadratic formula: x23x1=0 [11.2] Problem 5QQ: 5. Solve using any appropriate method:
.
[11.2]
Problem 1PTMO: Multiply and simplify. (x2i)(x+2i)[10.8] Problem 2PTMO: Multiply and simplify.
2. .
Problem 3PTMO: Multiply and simplify.
3.
Problem 4PTMO: Multiply and simplify. (x(3+5i))(x(35i))[10.8] format_list_bulleted