Characteristics of Quadratic Functions

Presentation

•

Mathematics

•

9th Grade

•

Hard

James Gonzalez

FREE Resource

21 Slides • 31 Questions

Quadratic Functions

Key Terms:

Examples!

Key Features of this Quadratic

Domain: All Real Numbers or −∞ < x < ∞
Range: [-4, ∞) or −4 ≤ y < ∞
X-intercept(s)/Zeros/Roots: (-3, 0) & (1, 0)
Y-intercept:(0, -3)
Vertex/Minimum: (-1,-4)
Axis of Symmetry: x = -1
Interval of Increase: x > -1
Interval of Decrease: x < -1
End Behavior:
- as x → −∞ , f(x) → ∞
- as x → ∞, f(x) → ∞

Domain Definition

the domain is the set of inputs accepted by the function

our x-values make up the domain

We can scan the x-axis from left to right to find our domain.

Range Definition

The range is our output values accepted by the function

therefore, y-values make up the range

Scan the y-axis from the bottom to the top to determine range.

Domain, Range, and End Behavior

Please write this review information down in your notebook. Draw the pictures. They do NOT have to be perfect, just a sketch. Follow the steps from the video.

Drag and Drop

What is the Domain?

Drag these tiles and drop them in the correct blank above

Drag and Drop

What is the Range?

≤

Drag these tiles and drop them in the correct blank above

Drag and Drop

What is the End Behavior?

As x → −∞ , f(x) →

As x → ∞, f(x) →

Drag these tiles and drop them in the correct blank above

Hotspot

Select the y-intercept.

Fill in the Blanks

What is the y-intercepts?

Multiple Choice

How many x-intercepts?

Hotspot

Select the x-intercepts.

Fill in the Blanks

What are the x-intercepts?

Hint: Enter the order pairs from Left to Right.

Dropdown

What are the zeros?

Hint: Enter the values from Left to Right.

x =

and x =

Hotspot

Select the vertex.

Fill in the Blanks

What is the vertex?

Multiple Choice

What is the vertex?

Maximum

Minimum

Drag and Drop

Use the graph above and find the axis of symmetry.

x =

Drag these tiles and drop them in the correct blank above

-1

-3

-2

-4

-5

Graphing

Use the graph above and drow the axis of symmetry.

Hint: Let one point be the vertex and the other point fall on the x-axis.

Drag and Drop

Use the graph above and find the intervals.

Interval of Increase:

Interval of Decrease:

Drag these tiles and drop them in the correct blank above

x < -1

x > -1

Poll

How do you feel about characteristics of quadratic functions?

I'm clueless

I need more practice

I got this!

Key Features of this Quadratic (Real World)

Domain: [0,40]
Range: [0,800]
Maximum: (20,800)
Zeros: (0,0) and (40,0)
Interval of Increase: 0 < x < 20
Interval of Decrease 20 < x < 40

Fill in the Blanks

The vertex of a parabola is the highest or lowest point on the parabola. The vertex for D(x) is (4, 2).

What is the vertex of B(x)?

Dropdown

The vertex for D(x) is (4, 2). The dolphin reaches a maximum height of 2 meters at 4 seconds.

What does the vertex of B(x) mean in context?

The Bird reaches a

height of

meters at

seconds

Drag and Drop

The axis of symmetry of D(x) is x = 4. This is the x value that splits the graph into 2 equal pieces.

What is the axis of symmetry of B(x)?

x =

Drag these tiles and drop them in the correct blank above

-1

Hotspot

The x-intercepts (or zeros or roots) of a function are the point(s) where the function crosses or touches the x-axis. The x-intercepts of B(x) are (1, 0) and (5, 0). This means that the height of the bird above sea level was 0 meters at 1 second and 5 seconds.

What are the x-intercepts of D(x)?

Fill in the Blanks

The x-intercepts of B(x) are (1, 0) and (5, 0).
What are the x-intercepts of D(x)?

Hint: Enter the order pairs from Left to Right.

Dropdown

The x-intercepts of B(x) are (1, 0) and (5, 0). This means that the height of the bird at sea level was 0 meters at 1 second and 5 seconds.

What does the x-intercepts of D(x) mean in context?

This means that the height of the dolphin at sea level was 0 meters at

second and

seconds.

Hotspot

The y-intercept of a function is the point that crosses the y-axis. This is also called the initial (start) value. The y-intercept of D(x) is (0, -6). This means at the start the dolphin was 6 meters below sea level.

What is the y-intercepts of B(x)?

Fill in the Blanks

The y-intercept of D(x) is (0, -6). This means at the start the dolphin was 6 meters below sea level.

What is the y-intercepts of B(x)?

Dropdown

The y-intercept of D(x) is (0, -6). This means at the start the dolphin was 6 meters below sea level.

What does the y-intercept of D(x) mean in context?

This means at the start the bird was

meters

sea level.

Dropdown

Function D(x) has an interval of increase when 0 ≤ x < 4 because the dolphin’s height is going up between 0 and 4 seconds.

What are the intervals of increase for B(x)?

Function B(x) has an interval of increase when

≤ x <

because the height of the bird is going up between

seconds and

seconds.

Dropdown

Function D(x) has an interval of decrease of

when 4 < x ≤ 7 because the height of the dolphin is going down between 4 seconds and 7 seconds.

What are the intervals of decrease for B(x)?

Function B(x) has an interval of decrease of

when

< x ≤

because the height of the bird is going down between

seconds and

seconds.

Drag and Drop

The domain of D(x) is 0 ≤ x ≤ 7 (0 to 7 seconds)
What are the domain of B(x)?

≤

(

seconds)

Drag these tiles and drop them in the correct blank above

Drag and Drop

The range of D(x) is –6 ≤ y ≤ 2 (6 meters below sea level to 2 meters above sea level).
What are the range of B(x)?

≤

meters below sea level to

meters above sea level

Drag these tiles and drop them in the correct blank above

-4

-2

-1

Categorize

Options (12)

The y-intercept of b(x) is (0, 6)

b(4) = 10

The height of the banana is decreasing on the interval 2.5 < x ≤ 6.

The vertex of the function is at (3, 12).

The banana reaches a maximum height of approximately 12.25 feet.

The banana is launched from a cannon 6 feet above the ground.

The interval of increase of the function is 0<x<4.

When the banana is 5 meters from the cannon, it is 8 meters above the

ground.

The banana has reached the same height as the cannon when it was 5 feet away from the cannon.

b(x) has a domain of 0 ≤ x ≤ 6.

The banana reaches the ground 5 feet from the cliff.

The function has an axis of symmetry at x = 2.5.

Sort the following statements into two categories(True or False).

True

False

Labeling

Closing:

Label the following characteristics on the graph.

Drag labels to their correct position on the image

vertex

maximum

y-intercept

x-intercept

minimum

Quadratic Functions

Key Terms:

Show answer

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