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OAT Lesson 24: Quadratic Equations

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Last updated almost 3 years ago
20 questions
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Activity 1: Graph it on Desmos

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Lesson Synthesis: - (5 min)

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

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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?
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)

Question 1
1.

Question 2
2.

Question 3
3.

Question 4
4.

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)
Question 5
5.

Solve for x:

Question 6
6.

Solve for x:

Question 7
7.

Solve for x:

Question 8
8.

Solve for x:

For this activity we'll experiment manipulating the quadratic equations on desmos.
Question 9
9.

Graph the function below:


Create a slider for "a" between -1 and 1

Explain what is happening?

Question 10
10.

Graph the function below:

y=x^2+a

Create a silder for "a"
What shape does the graph make?

Question 11
11.

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:
Question 12
12.

Factor Completely:

Question 13
13.

Factor Completely:

Question 14
14.

Solve for x:

Question 15
15.

Solve for x:

Question 16
16.

Solve for x:

Today you learned about a new kind of function called a quadratic.
Question 17
17.

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?

Question 18
18.

Solve for x:

Question 19
19.

Factor Completely:

Question 20
20.

Solve for x: