Unit 8

Quadratic Equations

Section A

Finding Unknown Inputs

1

Finding Unknown Inputs

Let’s find some new equations to solve.

2

When and Why Do We Write Quadratic Equations?

Let’s try to solve some quadratic equations.

Section A

Finding Unknown Inputs

1

Finding Unknown Inputs

Let’s find some new equations to solve.

2

When and Why Do We Write Quadratic Equations?

Let’s try to solve some quadratic equations.

Section B

Solving Quadratic Equations

3

Solving Quadratic Equations by Reasoning

Let’s find solutions to quadratic equations.

4

Solving Quadratic Equations with the Zero Product Property

Let’s find solutions to equations that contain products that equal zero.

5

How Many Solutions?

Let’s use graphs to investigate quadratic equations that have two solutions, one solution, or no solutions.

6

Rewriting Quadratic Expressions in Factored Form (Part 1)

Let’s write expressions in factored form.

7

Rewriting Quadratic Expressions in Factored Form (Part 2)

Let’s write some more expressions in factored form.

8

Rewriting Quadratic Expressions in Factored Form (Part 3)

Let’s look closely at some special kinds of factors.

9

Solving Quadratic Equations by Using Factored Form

Let’s solve some quadratic equations that, before now, we could only solve by graphing.

10

Rewriting Quadratic Expressions in Factored Form (Part 4)

Let’s transform more-complicated quadratic expressions into the factored form.

Section B

Solving Quadratic Equations

1

Solving Quadratic Equations by Reasoning

Let’s find solutions to quadratic equations.

2

Solving Quadratic Equations with the Zero Product Property

Let’s find solutions to equations that contain products that equal zero.

3

How Many Solutions?

Let’s use graphs to investigate quadratic equations that have two solutions, one solution, or no solutions.

4

Rewriting Quadratic Expressions in Factored Form (Part 1)

Let’s write expressions in factored form.

5

Rewriting Quadratic Expressions in Factored Form (Part 2)

Let’s write some more expressions in factored form.

6

Rewriting Quadratic Expressions in Factored Form (Part 3)

Let’s look closely at some special kinds of factors.

7

Solving Quadratic Equations by Using Factored Form

Let’s solve some quadratic equations that, before now, we could only solve by graphing.

8

Rewriting Quadratic Expressions in Factored Form (Part 4)

Let’s transform more-complicated quadratic expressions into the factored form.

Section C

Completing the Square

11

What Are Perfect Squares?

Let’s see how perfect squares make some equations easier to solve.

12

Completing the Square (Part 1)

Let’s learn a new method for solving quadratic equations.

13

Completing the Square (Part 2)

Let’s solve some harder quadratic equations.

14

Completing the Square (Part 3)

Let’s complete the square for some more complicated expressions.

15

Quadratic Equations with Irrational Solutions

Let’s find exact solutions to quadratic equations, even if the solutions are irrational.

Section C

Completing the Square

1

What Are Perfect Squares?

Let’s see how perfect squares make some equations easier to solve.

2

Completing the Square (Part 1)

Let’s learn a new method for solving quadratic equations.

3

Completing the Square (Part 2)

Let’s solve some harder quadratic equations.

4

Completing the Square (Part 3)

Let’s complete the square for some more complicated expressions.

5

Quadratic Equations with Irrational Solutions

Let’s find exact solutions to quadratic equations, even if the solutions are irrational.

Section D

The Quadratic Formula

16

The Quadratic Formula

Let’s learn a formula for finding solutions to quadratic equations.

17

Applying the Quadratic Formula (Part 1)

Let’s use the quadratic formula to solve some problems.

18

Applying the Quadratic Formula (Part 2)

Let’s use the quadratic formula and solve quadratic equations with care.

19

Deriving the Quadratic Formula

Let’s find out where the quadratic formula comes from.

20

Rational and Irrational Solutions

Let’s consider the kinds of numbers we get when solving quadratic equations.

21

Sums and Products of Rational and Irrational Numbers

Let’s make convincing arguments about why the sums and products of rational numbers and irrational numbers are always certain kinds of numbers.

Section D

The Quadratic Formula

1

The Quadratic Formula

Let’s learn a formula for finding solutions to quadratic equations.

2

Applying the Quadratic Formula (Part 1)

Let’s use the quadratic formula to solve some problems.

3

Applying the Quadratic Formula (Part 2)

Let’s use the quadratic formula and solve quadratic equations with care.

4

Deriving the Quadratic Formula

Let’s find out where the quadratic formula comes from.

5

Rational and Irrational Solutions

Let’s consider the kinds of numbers we get when solving quadratic equations.

6

Sums and Products of Rational and Irrational Numbers

Let’s make convincing arguments about why the sums and products of rational numbers and irrational numbers are always certain kinds of numbers.

Section E

Vertex Form Revisited

22

Rewriting Quadratic Expressions in Vertex Form

Let’s see what else completing the square can help us do.

23

Using Quadratic Expressions in Vertex Form to Solve Problems

Let’s find the maximum or minimum value of a quadratic function.

Section E

Vertex Form Revisited

1

Rewriting Quadratic Expressions in Vertex Form

Let’s see what else completing the square can help us do.

2

Using Quadratic Expressions in Vertex Form to Solve Problems

Let’s find the maximum or minimum value of a quadratic function.

Section F

Let's Put It to Work

24

Using Quadratic Equations to Model Situations and Solve Problems

Let’s analyze a situation modeled by a quadratic equation.

Section F

Let's Put It to Work

1

Using Quadratic Equations to Model Situations and Solve Problems

Let’s analyze a situation modeled by a quadratic equation.

Section A

Finding Unknown Inputs

1

Finding Unknown Inputs

Let’s find some new equations to solve.

2

When and Why Do We Write Quadratic Equations?

Let’s try to solve some quadratic equations.

Section F

Let's Put It to Work

24

Using Quadratic Equations to Model Situations and Solve Problems

Let’s analyze a situation modeled by a quadratic equation.

Section E

Vertex Form Revisited

22

Rewriting Quadratic Expressions in Vertex Form

Let’s see what else completing the square can help us do.

23

Using Quadratic Expressions in Vertex Form to Solve Problems

Let’s find the maximum or minimum value of a quadratic function.

Section C

Completing the Square

11

What Are Perfect Squares?

Let’s see how perfect squares make some equations easier to solve.

12

Completing the Square (Part 1)

Let’s learn a new method for solving quadratic equations.

13

Completing the Square (Part 2)

Let’s solve some harder quadratic equations.

14

Completing the Square (Part 3)

Let’s complete the square for some more complicated expressions.

15

Quadratic Equations with Irrational Solutions

Let’s find exact solutions to quadratic equations, even if the solutions are irrational.

Section D

The Quadratic Formula

16

The Quadratic Formula

Let’s learn a formula for finding solutions to quadratic equations.

17

Applying the Quadratic Formula (Part 1)

Let’s use the quadratic formula to solve some problems.

18

Applying the Quadratic Formula (Part 2)

Let’s use the quadratic formula and solve quadratic equations with care.

19

Deriving the Quadratic Formula

Let’s find out where the quadratic formula comes from.

20

Rational and Irrational Solutions

Let’s consider the kinds of numbers we get when solving quadratic equations.

21

Sums and Products of Rational and Irrational Numbers

Let’s make convincing arguments about why the sums and products of rational numbers and irrational numbers are always certain kinds of numbers.

Section B

Solving Quadratic Equations

3

Solving Quadratic Equations by Reasoning

Let’s find solutions to quadratic equations.

4

Solving Quadratic Equations with the Zero Product Property

Let’s find solutions to equations that contain products that equal zero.

5

How Many Solutions?

Let’s use graphs to investigate quadratic equations that have two solutions, one solution, or no solutions.

6

Rewriting Quadratic Expressions in Factored Form (Part 1)

Let’s write expressions in factored form.

7

Rewriting Quadratic Expressions in Factored Form (Part 2)

Let’s write some more expressions in factored form.

8

Rewriting Quadratic Expressions in Factored Form (Part 3)

Let’s look closely at some special kinds of factors.

9

Solving Quadratic Equations by Using Factored Form

Let’s solve some quadratic equations that, before now, we could only solve by graphing.

10

Rewriting Quadratic Expressions in Factored Form (Part 4)

Let’s transform more-complicated quadratic expressions into the factored form.

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Quadratic Equations

Unit 8 Resources

Finding Unknown Inputs

Finding Unknown Inputs

When and Why Do We Write Quadratic Equations?

Finding Unknown Inputs

Finding Unknown Inputs

When and Why Do We Write Quadratic Equations?

Solving Quadratic Equations

Solving Quadratic Equations by Reasoning

Solving Quadratic Equations with the Zero Product Property

How Many Solutions?

Rewriting Quadratic Expressions in Factored Form (Part 1)

Rewriting Quadratic Expressions in Factored Form (Part 2)

Rewriting Quadratic Expressions in Factored Form (Part 3)

Solving Quadratic Equations by Using Factored Form

Rewriting Quadratic Expressions in Factored Form (Part 4)

Solving Quadratic Equations

Solving Quadratic Equations by Reasoning

Solving Quadratic Equations with the Zero Product Property

How Many Solutions?

Rewriting Quadratic Expressions in Factored Form (Part 1)

Rewriting Quadratic Expressions in Factored Form (Part 2)

Rewriting Quadratic Expressions in Factored Form (Part 3)

Solving Quadratic Equations by Using Factored Form

Rewriting Quadratic Expressions in Factored Form (Part 4)

Completing the Square

What Are Perfect Squares?

Completing the Square (Part 1)

Completing the Square (Part 2)

Completing the Square (Part 3)

Quadratic Equations with Irrational Solutions

Completing the Square

What Are Perfect Squares?

Completing the Square (Part 1)

Completing the Square (Part 2)

Completing the Square (Part 3)

Quadratic Equations with Irrational Solutions

The Quadratic Formula

The Quadratic Formula

Applying the Quadratic Formula (Part 1)

Applying the Quadratic Formula (Part 2)

Deriving the Quadratic Formula

Rational and Irrational Solutions

Sums and Products of Rational and Irrational Numbers

The Quadratic Formula

The Quadratic Formula

Applying the Quadratic Formula (Part 1)

Applying the Quadratic Formula (Part 2)

Deriving the Quadratic Formula

Rational and Irrational Solutions

Sums and Products of Rational and Irrational Numbers

Vertex Form Revisited

Rewriting Quadratic Expressions in Vertex Form

Using Quadratic Expressions in Vertex Form to Solve Problems

Vertex Form Revisited

Rewriting Quadratic Expressions in Vertex Form

Using Quadratic Expressions in Vertex Form to Solve Problems

Let's Put It to Work

Using Quadratic Equations to Model Situations and Solve Problems

Let's Put It to Work

Using Quadratic Equations to Model Situations and Solve Problems

Finding Unknown Inputs

Finding Unknown Inputs

When and Why Do We Write Quadratic Equations?

Let's Put It to Work

Using Quadratic Equations to Model Situations and Solve Problems

Vertex Form Revisited

Rewriting Quadratic Expressions in Vertex Form

Using Quadratic Expressions in Vertex Form to Solve Problems

Completing the Square

What Are Perfect Squares?

Completing the Square (Part 1)

Completing the Square (Part 2)

Completing the Square (Part 3)