Lesson 6 Sorry, We’re Closed Develop Understanding

Ready

1.

a.

Graph $f (x) = \frac{2}{3} x + 4$ .

b.

Use the graph to find when $f (x) = 0$ .

c.

Use the graph to find the value of $f (0)$ .

2.

a.

Graph $g (x) = - \frac{1}{2} x + 3$ .

b.

Use the graph to find when $g (x) = 0$ .

c.

Use the graph to find the value of $g (0)$ .

3.

a.

Graph $h (x) = x^{2} - 2 x - 15$ .

b.

Use the graph to find when $h (x) = 0$ .

c.

Use the graph to find the value of $h (0)$ .

d.

Find the minimum value of $h (x)$ .

4.

a.

Graph $k (x) = 9 - x^{2}$ .

b.

Use the graph to find when $k (x) = 0$ .

c.

Use the graph to find the value of $k (0)$ .

d.

Find the minimum or maximum value of $k (x)$ . Indicate whether it’s a minimum or a maximum.

Set

5.

Give an argument for the statement: The sum of the integers $521$ and $1, 342$ is always odd. (Consider the case where one of the given integers is negative.) Then write a statement about the sum of even and odd integers.

6.

Write the polynomials that are analogous to the integers $521$ and $1, 342$ .

7.

Given two polynomials $P (x)$ and $Q (x)$ .

The constant term in $P (x)$ is even and the constant term of $Q (x)$ is odd. Would it be correct to assert that the constant term of $P (x) \pm Q (x)$ would be odd? Explain.

Identify the following statement as sometimes true, always true, or never true.

If your answer is sometimes true, give an example of when it’s true and an example of when it’s not true.
If it’s never true, give a counterexample.

8.

The set of linear polynomials is closed under multiplication.

9.

The set of all polynomials is closed under multiplication.

10.

The set of cubic polynomials is closed under subtraction.

11.

The set of all polynomials is closed under subtraction.

12.

The set of all polynomials is closed under division.

Go

Solve each quadratic equation.

13.

$x^{2} - 8 x = 33$

14.

$x^{2} - 21 = - 4 x$

15.

$x^{2} - 2 x = 74$

16.

$x^{2} - 5 x + 2 = 0$

17.

$2 x^{2} - 7 x - 4 = 0$

18.

$3 x^{2} - 4 x + 2 = 0$