Characteristics of Quadratics

​Introduction to Parabolas!

• ​Put away all devices/headphones

• Add your name/date/topic to your cornell notes

• Open STAAR Desmos Graphing Calculator

• Have a pencil ready

Poll

Have you heard the word parabola before?

• Yes!

• No...

​These are all parabolas. How can you describe them? Talk with the people at your table for one minute.

Word Cloud

Where have you seen a parabola in real life?

The direction of a quadratic describes how it opens: up or down ​

​

"A smile or a frown"​

Multiple Choice

What is the direction of the parabola?

• Opens Up

• Opens Down

• Opens Left

• Opens Right

Multiple Choice

What is the direction of the parabola?

$$y=3x^2-7x+8$$  

• Opens Up

• Opens Down

• Opens Left

• Opens Right

The "turning point"​

• The vertex of ​a quadratic is the point where the quadratic changes direction

Minimum or Maximum​

• The vertex can also be thought as the highest or lowest number.

• The minimum or maximum of a parabola is a number. Specifically, It is the y value of the vertex.

Multiple Select

Identify the vertex and then tell whether it's a minimum or maximum. Select two answer choices.

• (0,0)

• (1,0)

• (0.5,-1)

• Minimum

• Maximum

Multiple Select

Identify the vertex and then tell whether it's a minimum or maximum. Select two answer choices.

$$-x^2+10x-24$$

• (-4,0)

• (5,1)

• (6,0)

• Minimum

• Maximum

Multiple Choice

What is the maximum value of the quadratic?

• 3

• 0

• 4

• 1

• 5

Fill in the Blank

The table represents a quadratic function. Which point is the vertex?

(Remember vertex is the "turning point")

*Type a coordinate point

"Cuts the parabola in half"​

• The axis of symmetry is a vertical line that cuts the parabola in half

• The axis of symmetry is always in the form (x = a number)

• The number is the x-value of the vertex

Fill in the Blank

What is the axis of symmetry for the quadratic function shown?

*Type a line

Fill in the Blank

What is the axis of symmetry for the quadratic function shown?

*Type a line

"Touches the x-axis"​

• The x-intercept of a parabola is the point where the parabola intersects the x-axis

• A parabola can have one, two or zero x-intercepts

​Notice the y value of the x-intercept is always 0.

Solutions, Zeros, and Roots

• Once we have the x-intercept, we can identify the solutions of the quadratics. They are just the x-value of the x-intercept(s).

• Solutions, zeroes, and roots all mean the same thing!

Multiple Select

Identify the solutions of the quadratic shown

*May be more than one answer

• 5

• 1

• 0

• 3

• -4

Multiple Select

Identify the zeroes of the following quadratic

$$\left(x-3\right)^2$$  

*May be more than one answer.

• 0

• 3

• 9

• There are none.

Multiple Choice

How many roots can be identified from the quadratic table shown?

 

• None

• One

• Two

• Three

Open Ended

Summarize everything that you learned today.

Poll

How are you feeling with what we've covered so far?

• I feel great!

• I feel good.

• I don't feel good.

• I feel horrible.