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Algebra 1

9.10.5 Different Forms of Quadratic Expressions

Algebra 19.10.5 Different Forms of Quadratic Expressions

9.10.5 Different Forms of Quadratic Expressions

9.10.5 • Different Forms of Quadratic Expressions

Activity

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the data card:

  1. Silently read the information on your card.
  2. Ask your partner, "What specific information do you need?" and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
  3. Before telling your partner the information, ask, "Why do you need to know (that piece of information)?"
  4. Read the problem card and solve the problem independently.
  5. Share the data card and discuss your reasoning.

If your teacher gives you the problem card:

  1. Silently read your card and think about what information you need to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain to your partner how you are using the information to solve the problem.
  4. When you have enough information, share the problem card with your partner, and solve the problem independently.
  5. Read the data card and discuss your reasoning.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

1. Use the information about functions ff and gg to answer the questions.

  • Function ff is defined by (x+3)(x+9)(x+3)(x+9).
  • Function gg is defined by (x+6)2−1(x+6)2−1.

a. Write an expression in vertex form (of a quadratic expression) that could define a quadratic function, ff.

b. Write an expression in factored form that could define a quadratic function, gg.

c. Show that ff and gg do not define the same function.

2. Functions aa and bb are quadratic functions.

Function aa is defined by (x−5)2−4(x−5)2−4.

Function bb is defined by (x+1)(x−5)(x+1)(x−5).

a. What are the zeros of function aa? Select two.

b. What is the xx-coordinate of the vertex (of a graph) representing function bb?

c. What is the yy-coordinate of the vertex of the graph representing function bb?

d. Show that aa and bb do not define the same function.

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