Different Forms of Quadratic Expressions

9.10.5 Different Forms of Quadratic Expressions

9.10.5 • Different Forms of Quadratic Expressions

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:

Silently read the information on your card.
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!)
Before telling your partner the information, ask, "Why do you need to know (that piece of information)?"
Read the problem card and solve the problem independently.
Share the data card and discuss your reasoning.

If your teacher gives you the problem card:

Silently read your card and think about what information you need to answer the question.
Ask your partner for the specific information that you need.
Explain to your partner how you are using the information to solve the problem.
When you have enough information, share the problem card with your partner, and solve the problem independently.
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 $f$ and $g$ to answer the questions.

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

Compare your answer:

$f (x) = (x + 6)^{2} - 9$

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

Compare your answer:

$g (x) = (x + 7) (x + 5)$

c. Show that $f$ and $g$ do not define the same function.

Compare your answer:

Rewriting $g$ in standard form gives $x^{2} + 12 x + 35$ , but $f$ is $x^{2} + 12 x + 27$ .

2. Functions $a$ and $b$ are quadratic functions.

Function $a$ is defined by $(x - 5)^{2} - 4$ .

Function $b$ is defined by $(x + 1) (x - 5)$ .

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

The correct answers are: $x = 3$ and $x = 7$ . The zeros of $a$ are $x = 3$ and $x = 7$ .

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

The $x$ -coordinate of the vertex is 2.

c. What is the $y$ -coordinate of the vertex of the graph representing function $b$ ?

The $y$ -coordinate of the vertex is -9.

d. Show that $a$ and $b$ do not define the same function.

Compare your answer:

Rewriting $a$ in standard form gives $x^{2} - 10 x + 21$ , and $b$ in standard form is $x^{2} - 4 x - 5$ .