Characteristics of Quadratic Functions

x

y

X-Intercd

X-Interc

Vertex

x-intercept

X-Interc

x-intercept

axis of symmetry

X-Interc

y-intercept

X-Intercepts:

Y-Intercept:

Vertex:

Axis of Symmetry:

End Behavior:

Mini-Lesson

Characteristics of Quadratic Functions

x

y

X-Intercd

X-Interc

Vertex

x-intercept

X-Interc

x-intercept

axis of symmetry

X-Interc

y-intercept

X-Intercepts:

Y-Intercept:

Vertex:

Axis of Symmetry:

End Behavior:

(-1, 0) and (5, 0)

(0, 5)

(2, 9)

x = 2

x → ∞ , f(x) → -∞

x → -∞ , f(x) → -∞

Characteristics of Quadratic Functions

x

y

Domain

​

Set Notation:

​

​

​

Interval Notation:

Domain: “What are the possible x-values where the graph exists?”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Domain

​

Set Notation:

​

​

​

Interval Notation:

Domain: “What are the possible x-values where the graph exists?”

All real numbers

(-∞, ∞)

-∞

∞

Characteristics of Quadratic Functions

x

y

Range

​

Set Notation:

​

​

​

Interval Notation:

Range: “What are the possible y-values where the graph exists?”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Range

​

Set Notation:

​

​

​

Interval Notation:

Range: “What are the possible y-values where the graph exists?”

{y|y ≤ 9}

(-∞, 9]

-∞

9

Characteristics of Quadratic Functions

x

y

Interval of Increase

​

Set Notation:

​

​

​

Interval Notation:

Interval of Increase: “When reading from left to right, where does �the graph go UP?”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Interval of Increase

​

Set Notation:

​

​

​

Interval Notation:

Interval of Increase: “When reading from left to right, where does �the graph go UP?”

{ x | x < 2 }

(-∞, 2)

-∞

2

Characteristics of Quadratic Functions

x

y

Interval of Decrease

​

Set Notation:

​

​

​

Interval Notation:

Interval of Decrease: “When reading from left to right, where does �the graph go DOWN?”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Interval of Decrease: “When reading from left to right, where does �the graph go DOWN?”

∞

2

Interval of Decrease

​

Set Notation:

​

​

​

Interval Notation:

{ x | x > 2 }

(2, ∞)

Characteristics of Quadratic Functions

x

y

Interval of Positive

​

Set Notation:

​

​

​

Interval Notation:

Interval of Positive: “Where are the y-values greater than zero? �(Look ABOVE the x-axis)”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Interval of Positive

​

Set Notation:

​

​

​

Interval Notation:

Interval of Positive: “Where are the y-values greater than zero? �(Look ABOVE the x-axis)”

5

-1

{ x | -1 < x < 5 }

(-1, 5)

-∞

∞

Characteristics of Quadratic Functions

x

y

Interval of Negative

​

Set Notation:

​

​

​

Interval Notation:

Interval of Negative: “Where are the y-values less than zero? �(Look BELOW the x-axis)”

Mini-Lesson

Characteristics of Quadratic Functions

x

y

Interval of Negative

​

Set Notation:

​

​

​

Interval Notation:

Interval of Negative: “Where are the y-values less than zero? �(Look BELOW the x-axis)”

{ x | x < -1 and x > 5 }

(-∞, -1) and (5, ∞)

5

-1

Characteristics of Quadratic Functions

Use the foldable to identify the following key characteristics.

Interval of Negative

​

Set Notation:

​

​

​

x

y

Characteristics of Quadratic Functions

Use the foldable to identify the following key characteristics.

Interval of Decrease

​

Interval Notation:

x

y

Characteristics of Quadratic Functions

Use the foldable to identify the following key characteristics.

Interval of Positive

​

Interval Notation:

Characteristics of Quadratic Functions

Use the foldable to identify the following key characteristics.

Domain

​

Interval Notation: