Worksheet onquadratic equations and their graphs

Instructions:

  1. Each person must fill out their own copy of this worksheet.
  2. Write all your answers on the worksheet itself.
  3. Use your textbook and talk with your classmates to help you complete this assignment.
  4. When you finish, place your completed work in the metal basket on the desk of the secretary (Patty von Behren) in building 18. This must be done before she leaves on Friday (usually around 4 PM). If the basket is getting full, look in my mailbox for one of the folders that had the originals, and put your worksheet in the folder for your hour.
  5. If for some reason you cannot turn in the assignment in person, you may email it to me or fax it to the number listed on the syllabus. The 4 PM Friday deadline still applies.

NOTE: You will probably not finish this entire worksheet in class, which is why it is your homework for Friday. This worksheet is the ONLY thing due on Friday.

  1. Write the sentence or phrase from the book that states the relationship between a “quadratic function” and a “parabola.” List the number of the page that contains the phrase you wrote.
  1. The textbook claims a quadratic function can always be written in what form?
  1. Show that the function written can be rewritten in the form listed for question #2. This requires you to show how to finish the multiplication .

For this function, list the values for a: _____, b: _____, and c: ______.

  1. Complete the following data table, and create an accurate graph of the basic quadratic function .

x / Q(x)
– 3
– 2
– 1
0
1
2
3
  1. Look at your graph of Q(x). Describe two ways it differs from the shape of the absolute value function’s graph. One of your descriptions should refer to differences at or near the vertex.
  1. Why does it make sense to call the line through the vertex “the axis of symmetry?” (What symmetry should you notice in the graph?)
  1. Copy your values for Q(x) from the previous table, and complete the new column to show the difference (change) between subsequent values of Q(x).

x / Q(x) / Change from previousQ(x)value / Magnitude (size) of change
– 3 / Cannot calculate
– 2
– 1 / – 3 / 3
0
1
2 / 3
3 / 5

Look back at your graph of Q(x), or at the blue curves graphed on page 639. The numbers in the “magnitude” column of the table above can be used to count grid squares for plotting the points of your graph. Use words and a sketch of the right half of the Q(x) graph to show how to use the “magnitude” number pattern to place points.

  1. On page 639, the book talks about functions . In your own words, explain what k stands for.

a)Write three different functions of the form described above. (Hint: See Example 1.)

b)Pick one of the functions you listed in part (a) – make sure it’s not one from the textbook example – and complete the data table and graph below. If necessary, change the scale of the graph to show all points from the table.

x / f(x) =
– 3
– 2
– 1
0
1
2
3

c)Suppose that someone doesn’t want to calculate a table of values to create the graph of your f(x) function. Write in words what you would tell him or her to do to the graph of Q(x) that would enable the person to obtain this new graph with little or no calculating.

  1. The purple box and Example 2 on page 640 show a way to write formulas so you can look at a certain number and have positive mean “go right” while negative means “go left” (just like the setup of the x-axis).

a)List two ways that the formula for F(x) given in Example 2b differs from the pattern in the purple box.

b)Look at the solution to 2b. The explanation seems very complicated, but the point is to help you see the value of h in this example. What is that value? h = ______

c)Why does this value of h make it easier to remember to move the y = x2 one space to the left?

d)Rewrite the function in homework problem #8 like the book did for F(x) in Example 2b, then describe how the vertex should be moved to graph the function in problem 8.

  1. Look at the information on page 642. When the book talks about a function , does the lack of a visible negative sign mean there are only shortcut rules when the coefficient of x2is a positive number?

How do the descriptions and examples on page 642 answer the above question? Include specific information (phrases, symbols) from the text in your response.

  1. Read through Example 5; it shows how to take a function in the form and create a reasonable sketch of its graph without filling out an x-y table. In the space below, explain the steps you need to follow in order to graph any quadratic whose formula follows the pattern above without filling out an x-y table.

[If it helps, you may want to start by writing what you would tell someone else to do in order to graph the specific function . To check your answer on this, compare your sketch with what the calculator produces.]

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