Lesson 1 ET on the Run Develop Understanding

Ready

Draw an area model that would represent each set of factors. Then, multiply each set of factors.

1.

$(x + 2) (x + 3)$

Multiplied form:

2.

$(x + 1) (x + 5)$

Multiplied form:

3.

$(x + 2) (x + 4)$

Multiplied form:

4.

$(x + 1) (x + 1)$

Multiplied form:

5.

$(x - 1) (x - 1)$

Multiplied form:

6.

$(x + 1) (x - 1)$

Multiplied form:

7.

a.

Use your area model for problem 5 to show where you see the $- 2 x$ .

b.

Use your area model for problem 5 to show where you see the $+ 1$ .

8.

a.

Use your area model for problem 6 to show why there is not a term that contains $x$ .

b.

Use your area model for problem 6 to show where you see the $- 1$ .

Set

9.

The graphs of $f (x) = x^{2}$ and $g (x) = - 2$ are shown on the same coordinate grid. (scale = $1$ )

a.

Graph the sum of $f (x)$ and $g (x)$ on the same grid.

b.

What is the basic shape of the new graph?

c.

Describe the transformation on $f (x)$ .

d.

Let’s call the new graph $h (x)$ . Identify the following features of $f (x)$ and $h (x)$ .

Feature	$f (x)$	$h (x)$
Vertex
Equation of axis of symmetry
$x$ -intercept(s)
$y$ - intercept(s)
Maximum or minimum?
What stayed the same and what changed?

e.

Write the equation of $h (x)$ .

10.

The graphs of $j (x) = x^{2}$ and $k (x) = - 2 x$ are shown on the same coordinate grid. (scale = $1$ )

a.

Graph the sum of $j (x)$ and $k (x)$ on the same grid.

b.

What is the basic shape of the new graph?

c.

Describe the transformation on $j (x)$ .

d.

Let’s call the new graph $m (x)$ . Identify the following features of $j (x)$ and $m (x)$ .

Feature	$j (x)$	$m (x)$
Vertex
Equation of axis of symmetry
$x$ -intercept(s)
$y$ - intercept(s)
Maximum or minimum?
What stayed the same and what changed?

e.

Write the equation of $m (x)$ .

11.

The graphs of $p (x) = x^{2}$ and $q (x) = 2 x - 2$ are shown on the same coordinate grid. (scale = $1$ )

a.

Graph the sum of $p (x)$ and $q (x)$ on the same grid.

b.

What is the basic shape of the new graph?

c.

Describe the two things this transformation did on $p (x)$ .

d.

Let’s call the new graph $r (x)$ . Identify the following features of $p (x)$ and $r (x)$ .

Feature	$p (x)$	$r (x)$
Vertex
Equation of axis of symmetry
$x$ -intercept(s)
$y$ - intercept(s)
Maximum or minimum?
What stayed the same and what changed?

e.

Write the equation of $r (x)$ .

12.

Fill in the blank:

When you add a quadratic function and a linear function, the sum will always be a function.

Go

Identify the functions in the tables as linear, exponential, quadratic, or neither.

13.

$x$	$f (x)$
$1$	$1$
$2$	$7$
$3$	$17$
$4$	$31$
$5$	$49$

14.

$x$	$f (x)$
$1$	$80$
$2$	$40$
$3$	$20$
$4$	$10$
$5$	$5$

15.

$x$	$f (x)$
$1$	$0.012$
$2$	$0.12$
$3$	$1.2$
$4$	$12$
$5$	$120$

16.

$x$	$f (x)$
$1$	$- 37$
$2$	$- 32.5$
$3$	$- 28$
$4$	$- 23.5$
$5$	$- 19$