Key Features Recap

Key Features

A recap...

Key Features of Quadratic Functions

• Axis of symmetry

• Vertex: minimum or maximum

• Intercepts: x and y

• Intervals: increasing and decreasing

• Domain and range

• Rate of change given x-values

Determine the following:

Domain: all the x-values

-> always (- ∞, ∞) for non-story problems

Range: all the y-values

-> need the y-value of the vertex

-> [4, ∞)

Increasing Intervals

• Find the AoS and decide which side goes uphill (from L to R)

• Find the x-value of the vertex

• Is this the end or the start of the interval?

• It will either be (- ∞, #) or (#, ∞)

• Increasing: (1, ∞)

Decreasing Intervals

• Find the AoS and decide which side goes downhill (from L to R)

• Find the x-value of the vertex

• Is this the end or the start of the interval?

• It will either be (- ∞, #) or (#, ∞)

• Decreasing: (- ∞, 1)

Intercepts

• y-intercepts: hit the y-axis

• (0, 0)

• x-intercepts: hit x-axis

• (0, 0) and (1, 0)

Rate of Change (ROC)

• Find the rate of change [1, 2]

• Find the rate between x-values of 1 and 2

• Find points on graph and find the rise and the run

• Rise: 4 Run: 1

• ROC: 4/1 or 4

Multiple Choice

Identify the domain and range of the function.

• Domain: [-6, 2]

  Range: [-3, 5]

• Domain: (-∞, ∞)

  Range: [-3, 5]

• Domain: (-∞, ∞)

  Range: (-∞, -3]

• Domain: (-∞, ∞)

  Range: [-3, ∞)

Multiple Choice

What is the range for the function below?

• (- ∞, 4)

• (- ∞, 4]

• All real numbers

  (- ∞, ∞)

Multiple Choice

Is this point a max or min?

• max
• min

Multiple Choice

Name the x-intercept(s)?

• (0, 0)

• (2, 4)

• (0, 0) and (0, 4)

• (0, 0) and (4, 0)

Multiple Select

Domain is

• [-∞, ∞]

• (-∞, ∞)

• [4, ∞]

• (4, ∞)

Multiple Select

Range is

• [-∞, 4]

• [-∞, 4)

• [4, ∞)

• [-4, ∞)

Multiple Select

Name the y-intercept?

• (0, 0)

• (2, 4)

• (0, 4)

• (0, 0) and (4, 0)