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OAT Lesson 24: Quadratic Equations

Last updated over 2 years ago
20 questions
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)

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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Solve for x:

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Solve for x:

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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Factor Completely:

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Solve for x:

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Solve for x:

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Solve for x:

Lesson Synthesis: - (5 min)

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?