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

Fill in the Blanks

Describe the point where the area changes from increasing to decreasing.

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)

Fill in the Blanks

b. To find the x-intercepts of f(x), use the factored form of f(x) and solve the equation f (x) = 0.

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?