2. Equations and Inequalities

Solve Quadratic Equations by the Square Root Property

Quadratic Equations

Word Problems Using the Pythagorean Theorem - Example 2

Solving for 'X' ;  Quadratic Equation / Pythagorean Theorem - Example 1

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 - 10x

Solve each equation in Exercises 83–108 by the method of your choice.

2x^2 - x = 1

In Exercises 71–72, without solving the given quadratic equation, determine the number and type of solutions. 9x^2 = 2-3x

Solving Trigonometric Equations Using the Quadratic Formula - Example 2

Solve each equation in Exercises 83–108 by the method of your choice.

3x^2 = 60

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 - (2/3)x

Solve each equation in Exercises 15–34 by the square root property.

3x^2 = 27

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.

x^2 - 2x + 1 = 0

In Exercises 115–122, find all values of x satisfying the given conditions.

y1 = x - 1, y2 = x + 4 and y1y2 = 14

In Exercises 115–122, find all values of x satisfying the given conditions.

y = 2x^2 - 3x and y = 2

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 - 7x

Solving Word Problems in Distance, Rate, and Time Using Quadratics - Example 2

Word Problems Using the Pythagorean Theorem - Example 3

Solve each equation in Exercises 83–108 by the method of your choice.

x^2 - 6x + 13 = 0

Solve each equation in Exercises 83–108 by the method of your choice.

x^2 - 2x = 1

Solving a Quadratic Equation: Factoring a Simple Example

Using the Discriminant for Quadratic Equations

Use the Quadratic Formula

Solve each equation in Exercises 47–64 by completing the square.

3x^2 - 2x - 2 = 0

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Factoring Trinomials by Trial and Error - Ex 2

Solve each equation in Exercises 47–64 by completing the square.

x^2 - 6x - 11 = 0

Quadratic Equations - Completing the Square

Solve each equation in Exercises 15–34 by the square root property.

3x^2 - 1 = 47

Solve each equation in Exercises 83–108 by the method of your choice.

1/x + 1/(x + 3) = 1/4

 Definition of A Quadratic Equation In One Variable

Algebra II: Quadratic Equations (Level 3 of 3)

Solving for 'X' ;  Quadratic Equations Involving the Pythagorean Theorem - Example 3

Algebra II: Quadratic Equations (Level 2 of 3)

Solve each equation in Exercises 47–64 by completing the square.

2x^2 - 7x + 3 = 0

Factoring Trinomials: Factor by Grouping - ex 1

Solve Quadratic Equations by Factoring a Trinomial / Example 2.8

Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation - Example 2

Solving Quadratic Equations using the Quadratic Formula - Example 3

Completing the Square Example 2 Solve Quad. Equations

Solve each equation in Exercises 83–108 by the method of your choice.

(2x - 5)(x + 1) = 2

Solve each equation in Exercises 83–108 by the method of your choice.

x^2 - 4x + 29 = 0

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.

2x^2 - 11x + 3 = 0

 Solve Quadratic Equations by Factoring a Trinomial / Example 2.7

Algebra II: Quadratic Equations - Factoring (Level 6 of 10)

Solving Quadratic Equations - Factoring and Using the Quadratic Formula

Solve each equation in Exercises 65–74 using the quadratic formula.

x^2 - 6x + 10 = 0

Completing the Square to Solve Quadratic Equations: More Examples - 4

Solving Trigonometric Equations Using the Quadratic Formula - Example 1

Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation - Example 3

Solve each equation in Exercises 83–108 by the method of your choice.

3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)

Using the Quadratic Formula

Solving Quadratic Equations using the Quadratic Formula - Example 1

Solving a Geometry Word Problem by Using Quadratic Equations - Example 1

Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation - Example 1

Completing the Square to Solve Quadratic Equations: More Examples - 1

Solve each equation in Exercises 1 - 14 by factoring.

3x^2 - 2x = 8

Derivation of the Quadratic Formula

Solve each equation in Exercises 1 - 14 by factoring.

2x(x - 3) = 5x^2 - 7x

Solve each equation in Exercises 15–34 by the square root property.

5x^2 = 45

Solving Quadratic Equations by Factoring - Basic Examples

 Using the Quadratic Formula

Create and solve quadratic equations

Solve each equation in Exercises 47–64 by completing the square.

3x^2 - 5x - 10 = 0

Algebra II: Quadratic Equations - Factoring (Level 9 of 10)

Solve each equation in Exercises 83–108 by the method of your choice.

5x^2 + 2 = 11x

The Zero-Product Property

Solve each equation in Exercises 1 - 14 by factoring.

10x - 1 = (2x + 1)^2 

In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression.

3/(2x^2 + 4x - 9)

Completing the Square to Solve Quadratic Equations: More Examples - 3

Solve each equation in Exercises 47–64 by completing the square.

x^2 + 4x + 1 = 0

Solve each equation in Exercises 83–108 by the method of your choice.

2x^2 - 7x = 0

Solve each equation in Exercises 83–108 by the method of your choice.

x^2 = 4x - 7

Solve each equation in Exercises 47–64 by completing the square.

x^2 - 5x + 6 = 0

Algebra II: Quadratic Equations - Factoring (Level 8 of 10)

Solving Quadratic Equations using the Quadratic Formula - Example 2, Complex Solutions

Example 4: Applying the quadratic formula | Quadratic equations

Solve each equation in Exercises 1 - 14 by factoring.

3x^2 + 12x = 0

Solve each equation in Exercises 83–108 by the method of your choice.

9 - 6x + x^2 = 0

Solving for 'X' ;  Quadratic Equations Involving the Pythagorean Theorem - Example 2

Solve each equation in Exercises 83–108 by the method of your choice.

(3x - 4)^2 = 16

Solving Trigonometric Equations Using the Quadratic Formula - Example 3

Solve each equation in Exercises 83–108 by the method of your choice.

4x^2 - 16 = 0

Solve each equation in Exercises 83–108 by the method of your choice.

2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)

Solve each equation in Exercises 47–64 by completing the square.

4x^2 - 4x - 1 = 0

Solve each equation in Exercises 47–64 by completing the square.

x^2 + 6x = 7

Solving Quadratic Equations by Completing the Square

Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0

In Exercises 115–122, find all values of x satisfying the given conditions.

y1 = - x^2 + 4x - 2, y2 = - 3x^2 + x - 1, and y1 - y2 = 0

In Exercises 115–122, find all values of x satisfying the given conditions.

y = 5x^2 + 3x and y = 2 

In Exercises 127–130, solve each equation by the method of your choice.

1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2 - 4)

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Solve quadratic equations by completing the square

Solve Quadratic Equations by Factorization / Example 2.6

Solving Word Problems involving Distance, Rate, and Time Using Quadratics - Example 3

Solve each equation in Exercises 83–108 by the method of your choice.

(2x + 3)(x + 4) = 1

 Solving Quadratic Equations Using the Square Root Method / Example 2.1

 Summary of Methods

Solve a quadratic equation: completing the square (2)

Solve a quadratic equation: taking a square root

IB Sample Exam Question, Paper 1 Q9

 Solve Quadratic Equations by Factoring a Trinomial / Example 2.9

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 + 3x

Completing the Square to Solve Quadratic Equations: More Examples - 2

Completing the Square to Solve Quadratic Equations: More Examples - 5

In Exercises 115–122, find all values of x satisfying the given conditions.

y1 = 2x^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0

Exercises 73–75 will help you prepare for the material covered in the next section.

Multiply: (7 - 3x)(- 2 - 5x)

In Exercises 115–122, find all values of x satisfying the given conditions.

y1 = 2x/(x + 2), y2 = 3/(x + 4), and y1 + y2 = 1

A Projectile Problem Using Quadratics - Example 1

Solving Quadratics by Completing the Square

Solve each equation in Exercises 47–64 by completing the square.

x^2 + 3x - 1 = 0

Determine the best method to solve a quadratic equation

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.

x^2 - 3x - 7 = 0

 Solving Quadratic Equations by Completing the Square / Example 2.3

Word Problems Using the Pythagorean Theorem - Example 1

In Exercises 127–130, solve each equation by the method of your choice.

√2 x^2 + 3x - 2√2 = 0

Factoring Trinomials (A quadratic Trinomial) by Trial and Error

❖ Completing the Square - Solving Quadratic Equations ❖

Deriving the Quadratic Formula

Solve each equation in Exercises 66–67 by completing the square. 3x^2 -12x+11= 0

Solve a quadratic equation using the quadratic formula

Understand the discriminant and nature of the roots

Completing the Square to Solve Quadratic Equations: More Examples - 6

Solve each equation in Exercises 83–108 by the method of your choice.

1/x + 1/(x + 2) = 1/3

Solving Quadratic Equations Using the Square Root Method / Example 2.2

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.

x^2 - 4x - 5 = 0

Solve each equation in Exercises 15–34 by the square root property.

2x^2 - 5 = - 55

 Solving Quadratic Equations by Completing the Square / Example 2.4

Solve each equation in Exercises 73–81 by the method of your choice. (x-3)^2 - 25 = 0

 Solve Quadratic Equations by Factorization / Example 2.5

Completing the Square to Solve a Quadratic Equation

 Simplification Techniques

Determine whether a number is real or imaginary: calculating the value of the discriminant

Exercises 100–102 will help you prepare for the material covered in the next section.

Factor: x^2 - 6x + 9

Solving a Geometry Word Problem by Using Quadratic Equations - Example 3

In Exercises 64–65, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2+ 20x

Solve each equation in Exercises 68–70 using the quadratic formula. 2x^2 = 3-4x

Solve a quadratic equation with no real solutions using the quadratic formula

Factoring Perfect Square Trinomials - Ex3

How to Solve Quadratic Equations - Using 3 Different Methods

Quadratic Equations - Factoring and Quadratic Formula

Solve each equation in Exercises 47–64 by completing the square.

x^2 - 2x = 2

Solve each equation in Exercises 47–64 by completing the square.

x^2 + 4x = 12

Solving a Projectile Problem Using Quadratics - Example 2

Factoring Perfect Square Trinomials - Ex1

How To Use the Quadratic Formula

Factoring Perfect Square Trinomials - Ex 2

Solving Word Problems in Distance, Rate, and Time Using Quadratics - Example 1

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 - (1/3)x

Solve a quadratic equation: using the quadratic formula

Solving a Geometry Word Problem by Using Quadratic Equations - Example 2

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