Graphing & Analyzing a Quadratic Function

Graphing & Analyzing a Quadratic Function

Objectives:

Graph a quadratic function.

Interpret key features of the graph of a quadratic function.

Take out a sheet of paper, and graph the table of values.

The graph of a quadratic function is a curve called a PARABOLA.

• A parabola has a point at which a maximum or minimum value of the function occurs.

• That point is called VERTEX OF A PARABOLA.

• The y-value of the vertex is the MAXIMUM OR MINIMUM of the function.

Multiple Choice

Identify the vertex of the graph. Does the vertex represent a maximum or a minimum of the function?

• (80, 6400) minimum

• (80, 6400) maximum

Multiple Choice

Examine the graph, for what values of the length is the area increasing and decreasing?

• The area is increasing between 1000 and 6000, and decreasing between 80 and 160

• The area is increasing between 0 and 80, and decreasing between 1000 and 6000

• The area is increasing between 0 and 80, and decreasing between 80 and 160

Open Ended

Use the table, the graph, and/or the function to determine the reasonable domain and range of the function A (l). Describe each using words.

Multiple Choice

Consider the quadratic function f(x) = x² - 2x -3.

a. Write the function in factored form by factoring the

polynomial x² - 2x -3.

• f (x) = ( x + 1) (x + 2)

• f (x) = ( x + 1) (x - 2)

• f (x) = ( x + 3) (x + 2)

• f (x) = ( x + 1) (x - 3)

Open Ended

c. A parabola is symmetric over the vertical line that contains the vertex. How do you think the x-coordinate of the vertex relates to the x-coordinates of the x-intercepts? Use the symmetry of a parabola to support your answer.

Multiple Choice

Write the vertex of the quadratic function.

• (4,-1)

• (-1, 4)

• (-4, 1)

• (1, -4)

Multiple Select

Complete the table for the

quadratic function f(x) = -x² - 4x - 3.

• f (x) = -3 , 0, 1, 0, -3

• f(x) = 3, 0, 1, 0, 3

Multiple Choice

Feelings about Quadratic Functions?