Warmup to 4.1

Quadratic Functions Exploration

On Thurs we will look in more detail about quadratic functions and the properties of the functions.  Read ahead, maybe watch a video, and go through the exploration given below to help you learn the material with understanding.

Follow the directions for the task given with the link and answer the following questions in the space provided.

http://members.shaw.ca/ron.blond/QFA.CSF.APPLET/index.html

http://robertfant.com/Java/GeoGebra/QuadraticVertexForm.htm

1)      Click on the following links and explore the graphs of quadratic functions in VERTEX FORM. 

a)      Describe what happens to the graph when you change the variable a.

(type here)

b)      Describe what happens to the graph when you change the variable h.

c)      Describe what happens to the graph when you change the variable k.

2)      Why do you think that vertex form was introduced in algebra?  Why didn’t we just stick to standard form?

3)      Would you prefer graphing a quadratic function in vertex form or in standard quadratic form?  Explain your answer.

4)      Let’s say a student in our class wants to know how to put a function given in standard quadratic form into VERTEX quadratic form, explain to this student how he/she could do this?  Explain the process ( you will be graded on thoughtful responses).

There are 2 ways of graphing quadratic functions: by transformations and by properties.

We’ve looked at graphing functions by transformations (in problems 1-4).  Now let’s look at graphing by properties.  You want to use graphing by properties when the function is in standard form.

5)      Here are the properties you need to know to in order to graph by properties.  Please go to the following link and put in the following function to find the properties.

http://www.wolframalpha.com/

Determine the vertex:

Determine the x-intercepts:

y-intercept:

equation of the line of symmetry

6)      Continue to use http://www.wolframalpha.com/

a)      Does the graph of this quadratic function open upwards or downwards?

b)      What is the vertex of the parabola?

c)      Does this function have a max or min value?

d)     Would this parabola have x-intercepts YES or NO? Explain why or why not?

Algebra is the study of patterns, making generalizations, and reasoning. What patterns do you see with graphing quadratics?