Unit 4: Frogs, Fleas, & Painted Cubes//Investigation 2//Connections

Name _______________________________________ Class ______________ Date ______________________________

Quadratic Expressions Connecting Your Knowledge

I can recognize and write equivalent quadratic expressions.

Math ______ / 30 points

Reflection _______ / 10 points

Total ______ / 40 Points

For this packet, your goal is to earn 40 points. 30 points will be from the math problems. 10 points will

be from the reflection section. Look at the point values of the following questions and answer the questions that you feel most comfortable to answer.

For Questions 1 and 2, draw a divided rectangle whose area is represented by each expression. Label the lengths and area of each section. Then write the expression in expanded form.

1. x(x + 7)

Divided Rectangle: Expanded Form:

2. x(x – 3) Divided Rectangle: Expanded Form: For Questions 3 and 4, draw a divided rectangle whose area is represented by each expression. Label the lengths and area of each section. Then write the expression in factored form.

3. x2 + 6x

Divided Rectangle: Factored Form:

2 points

2 points

2 points

4. x2 - 8x Divided Rectangle: Factored Form:

For Questions 5 and 6, write the expression in factored form:

5. x2 + 10x

Factored Form:

6. x2 - 6x Factored Form: For Questions 7 and 8, write the expression in expanded form:

7. x(x + 9)

Expanded Form:

8. x(x – 13) Expanded Form:

For Questions 9-10, write two expressions for the area of the large rectangle: one in factored form and one in expanded form.

9. Factored Form:

Expanded Form:

2 points

2 points

2 points

2 points

2 points

x

3

10 x

10. Factored Form:

Expanded Form: For Questions 11 and 12, write each expression in expanded form.

11. (x + 3)(x – 4)

12. (x + 7)2 For Questions 13 and 14, write each expression in factored form.

13. x2 - 10x + 24

14. x2 - 11x - 12 15. For the equation y = x2 + 5x + 6:

a. Write it in factored form:

b. Identify the x-intercepts:

c. Identify the y-intercept:

d. Find the coordinates of the maximum or minimum point:

e. Find the line of symmetry:

2 points

2 points

2 points

5 points

4

x

12 x

2 points

2 points

16. Corey makes a rectangle from a square by doubling one dimension and adding 4 centimeters. He leaves the other dimension unchanged.

a. What are the new dimensions (length and width) of the new rectangle, using (x) as the

original side length?

Length: Width:

b. Draw a rectangle with the new dimensions labeled.

c. Write an equation for the area of the new rectangle in terms of the side length (x) of the original square.

17. A rectangle has dimensions of length = (x) and width = (x +1) centimeters. a. What is the equation of the area of the rectangle?

b. The rectangle is enlarged by a scale factor of 2 (each dimension is doubled). What are the new dimensions?

Length: Width:

c. What is the equation of the area of the new rectangle?

18. Write 4x2 + 10x + 6 in factored form. You may want to draw a rectangle model to help you .

5 points

5 points

5 points

19. a. Create tables for the equations y = x2 + 2x and y = x2 + 2.

x y x y

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3

b. Sketch the graphs of each equation: c. How are the graphs similar?

d. How are the graphs different?

e. What are the y-intercepts of each graph?

f. What are the x-intercepts of each graph (if they exist)?

10 points

20. Match each equation with its graph. Then EXPLAIN how to locate the line of symmetry for each graph.

a. y = (x + 7)(x + 2) c. y = x2 + 3x b. y = x2 + 2x – 24 d. y = (x – 5)(x + 5)

10 points

Quadratic Expressions: Reflection

In this investigation, you wrote quadratic expressions to represent areas of rectangles formed by changing the dimensions of a square. You rewrote expressions in different forms by using rectangular models and by using the Distributive Property. You looked at the equations and graphs of functions. Answer the following questions in complete sentences. (This reflection is worth 10 of your total of 40 points.) 1. Suppose a quadratic expression is in factored form. How can you use the distributive property to

find an equivalent expression in expanded form? (Use an example) 2. Suppose a quadratic expression is in expanded form. How can you use the distributive property to

find an equivalent expression in factored form? (Use an example) 3. Describe what you know about the shape of the graph of a quadratic function. 4. What are important features of a quadratic graph? Be very specific! 5. How can you predict a quadratic graph’s important features from its equation? Be very specific!