OAT Lesson 24: Quadratic Equations

Last updated about 3 years ago

20 Nsɛmmisa

Lesson Synthesis: - (5 min)

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Today you learned about a new kind of function called a quadratic.

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OAT Lesson 24: Quadratic Equations

Last updated about 3 years ago

20 Nsɛmmisa

Develop Understanding

Today's Learning Goal: (G6, U6, L6)

Explain (orally) how to create and solve an equation that represents a situation with an unknown amount.
Write an expression with a variable to generalize the relationship between quantities in a situation.

Today's Materials:

Laptop
Laptop charger
Pen/Pencil/Paper/Expo Marker (optional)

Please complete the Jump Start (activator). You have 5 minutes before we review. This is independent it should be silent.

Reminders:

1. Ready for class

2. No cellphones

3. Volume must be low.

4. Read and follow all directions

5.) Take your bag off and immediately begin the Activator.

JUMP START: Algebra Talk: Positive Solutions - ( 5min)

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Launch: Intro to quadratic Equations - (10 min)

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I do (question

We do (question

You do (question)

Definition: a quadratic equation is an equation in which the highest degree of its variable is 2.

The inverse of a square x^2 is square root(x)

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Solve for x:

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Solve for x:

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Activity 1: Graph it on Desmos

For this activity we'll experiment manipulating the quadratic equations on desmos.

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Graph the function below:
Create a slider for "a" between -1 and 1
Explain what is happening?

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Graph the function below:
y=x^2+a
Create a silder for "a"
What shape does the graph make?

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Graph the function below:
and
Create a slider for "a"
What shape does the graph make?

Activity 2: Standard Form

When given a quadratic equation in the form:

where a, b, c are constants. We can use a method called Factoring to make this quadratic into linear equations.

Factoring method looks like this:

c = m*n and b= m+n.

We can also use this method to solve for a quadratic if its given to us in the form:

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Factor Completely:

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Lesson Synthesis: - (5 min)

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Today you learned about a new kind of function called a quadratic.

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What is the highest degree?
How do you find the coefficient b?
How do you find the coefficient c?
Where do you find quadratic equations?

Cool Down: Squares and Squares Roots - (5 min)

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Solve for x:

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Factor Completely:

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Solve for x:

Closure Questions:

What is a quadratic?

What is the inverse of a square?

What is a another name for a square root?

What is the method you learned today?

What is the shape that quadratic equation makes?

OAT Lesson 24: Quadratic Equations

Lesson Synthesis: - (5 min)

OAT Lesson 24: Quadratic Equations

JUMP START: Algebra Talk: Positive Solutions - ( 5min)

Launch: Intro to quadratic Equations - (10 min)

Solve for x:

Solve for x:

Activity 1: Graph it on Desmos

Graph the function below:Create a slider for "a" between -1 and 1 Explain what is happening?

Graph the function below:y=x^2+aCreate a silder for "a"What shape does the graph make?

Graph the function below:and Create a slider for "a"What shape does the graph make?

Activity 2: Standard Form

Factor Completely:

Lesson Synthesis: - (5 min)

What is the highest degree?How do you find the coefficient b?How do you find the coefficient c?Where do you find quadratic equations?

Cool Down: Squares and Squares Roots - (5 min)

Solve for x:

Factor Completely:

Solve for x:

Closure Questions:

JUMP START: Algebra Talk: Positive Solutions - ( 5min)

Launch: Intro to quadratic Equations - (10 min)

Solve for x:

Solve for x:

Solve for x:

Solve for x:

Activity 1: Graph it on Desmos

Graph the function below:Create a slider for "a" between -1 and 1 Explain what is happening?

Graph the function below:y=x^2+aCreate a silder for "a"What shape does the graph make?

Graph the function below:and Create a slider for "a"What shape does the graph make?

Activity 2: Standard Form

Factor Completely:

Factor Completely:

Solve for x:

Solve for x:

Solve for x:

What is the highest degree?How do you find the coefficient b?How do you find the coefficient c?Where do you find quadratic equations?

Cool Down: Squares and Squares Roots - (5 min)

Solve for x:

Factor Completely:

Solve for x:

Closure Questions:

Solve for x:

Solve for x:

Factor Completely:

Solve for x:

Solve for x:

Solve for x:

Graph the function below:
Create a slider for "a" between -1 and 1
Explain what is happening?

Graph the function below:
y=x^2+a
Create a silder for "a"
What shape does the graph make?

Graph the function below:
and
Create a slider for "a"
What shape does the graph make?

What is the highest degree?
How do you find the coefficient b?
How do you find the coefficient c?
Where do you find quadratic equations?

Graph the function below:
Create a slider for "a" between -1 and 1
Explain what is happening?

Graph the function below:
y=x^2+a
Create a silder for "a"
What shape does the graph make?

Graph the function below:
and
Create a slider for "a"
What shape does the graph make?

What is the highest degree?
How do you find the coefficient b?
How do you find the coefficient c?
Where do you find quadratic equations?