Lesson 2 I’ve Been Framed Develop Understanding

Ready

Multiply the given binomials. Write your answers in descending order of the exponent.

1.

$(x + 11) (x - 2)$

2.

$(x + 5) (x + 8)$

3.

$(x - 7) (x + 6)$

4.

$(2 x + 1) (x + 6)$

5.

$(- 3 x - 7) (2 x - 1)$

6.

$(2 x - 3) (5 x - 11)$

Set

7.

A cement pathway of uniform width is to be poured around a rectangular swimming pool measuring $24$ by $40 feet$ . What would be the area of the pathway if it was only $1 foot$ wide?

8.

Write an equation and complete the table to show the relationship between the area of the pathway $A (x)$ and the width of the pathway $x$ .

Width of path $(x) f t$	Area of path $A (x) f t^{2}$
$1$
$2$
$3$
$4$
$5$

9.

The homeowner can only afford to purchase up to $1,000 sq. feet$ of cement. Use the given graph to find the maximum width of the pathway (in whole feet) that the homeowner can afford.

10.

What kind of function is $A (x) ?$

How do you know?

11.

What is the domain of $A (x)$ if the owner decides to pour between $132$ and $740 sq.ft$ of cement?

12.

What is the range of $A (x)$ if the homeowner wants a pathway that is between $3 ft$ and $5 ft$ wide?

Go

Write the equation of a line perpendicular to the given line and passing through the given point.

13.

$y = 2 x + 10$

point $(2, - 8)$

14.

$y = - 3 x + 14$

point $(- 9, - 12)$

15.

$y = \frac{5}{6} x + 17$

point $(- 10, 20)$

16.

$y = - \frac{2}{3} x - 39$

point $(12, - 6)$