Domain & Range of Parabolas

Domain & Range of Parabolas

Essential Question

How can you determine if the range as a maximum or minimum value?

Lets begin...

In its simplest form the domain is all the values (X) that go into a function, and the range is all the values (Y)) that come out.

Inequality Symbols

This is how write the domain and range.

Inequality Notation

This is how write the domain and range.

Minimum vs Maximum

The minimum value is where a parabola begin and it opens upward.

The maximum value is where a parabola begins and it open downward.

The Vertex

The vertex is the point on a parabola were it changes direction. (The starting point)

The Axis of Symmetry

A vertical line that goes through the vertex (starting point).

Lets Practice

Students will determine the domain, range, line of symmetry, and vertex.

Multiple Choice

What is the Domain?

• -10 ≤ y ≤ 6

• y ≤ 6

• -10 ≤ x ≤ 6

• All Real Numbers

Multiple Choice

What is the Range?

• -3 ≤ y < 2

• -3 < y ≤ 2

• -7 ≤ y ≤ 2

• -7 ≤ y < 2

Multiple Choice

What is the Range?

• y ≥ 6

• y ≤ 6

• -10 ≤ y ≤ 6

• -10 ≤ x ≤ 6

Multiple Choice

What is the vertex of this function?

• (0, -3)

• (1, -4)

• (-2, 5)

• {-1, 3}

Multiple Choice

Does this function have a maximum or minimum?

• maximum

• minimum

Multiple Choice

What is the vertex?

• (4,-4)

• (2,0)

• (0,2)

• (6,0)

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

• symmetrical point for the vertex

Multiple Choice

Which best describes the vertex of a parabola?

• Any point on the parabola.

• A point on the x-axis.

• The highest or lowest point of a parabola

• A point on the y-axis.

Multiple Choice

What is the domain of the function?

• x≥3

• x≤3

• All real numbers

• -1≤x≤5

Multiple Choice

Does the quadratic have a max/min vertex, and does the parabola open up/down?

• max/ opens down
• min/ opens up
• max/ opens up
• min/ opens down

Multiple Choice

What is the range of the function?

• y≤3

• y≥3

• All real numbers

• -6≤y≤3

Multiple Choice

What is the green dot on the parabola called?

• maximum

• minumum

• roots

• zeros

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum

• Maximum

Multiple Choice

What is the range of the function?

• y < -1

• y > -1

• y < -2

• y > -2

Multiple Choice

The graph of a quadratic function is called a

• Parabola

• Vertex

• Axis of Symmetry

• Vertex Form

Open Ended

How can you determine if the range as a maximum or minimum value? (Hint: The minimum and maximum values are represented by.........so.........