Chapter 4 Take home quiz

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Date: ______. This is open notebook QUIZ. You may use books and notes, but you may NOT collaborate with anyone. 1. Chapter 4 Take home quiz. 1. Graph y  ...
Name: ______________________ Class: _________________ Date: _________ This is open notebook QUIZ. You may use books and notes, but you may NOT collaborate with anyone.

Chapter 4 Take home quiz 2

1. Graph y = 2x + x + 3. State the intercepts, axis of symmetry and vertex. Does it have a max or min? What it is?

2

2

2. How would you translate the graph of y = x to produce the graph of y = x + 10? 2

2

3. How would you translate the graph of y = x to produce the graph of y = ( x− 7 ) ? 2

4. The graph of the equation y = ax − 4x + c has vertex (2, 5). a. Explain how to use the formula for the x-coordinate of the vertex to find the value of a. b. Use the values of x and y from the vertex in the equation to find the value of c, then write the equation.

The equation is ________________________.

1

5. The height of a triangle is three feet longer than the base. The area of the triangle is 35 square feet. Find the height and base of the triangle. Sketch a picture showing variables. Write an equation and solve it.

height =

base =

6. A restaurant has a patio that is 8 feet wide and 12 feet long. The restaurant owners want to double the area of the patio by increasing the width and the length by the same distance x. Sketch a picture and label with varaible expressions. Write an equation that x must satisfy. Find the value for x.

The length and width must be increased by : 7. Factor.

2

16x − 25 2

8. Factor: 12h − 31h + 20 9. Factor completely.

4

3

12y + 100y + 112y

2

2

10. Solve for x

2

−3 ( x + 9 ) = −63

x= 1 2 1 11. Solve using the quadratic formula. Then write the answer to two decimal places. − x + 5 = 2 6

x= 12. Simplify

6 4+

2

.

Ê 13. Solve the equation ÁÁÁÁ x + Ë

2

˜ˆ˜ ÁÊÁ x − ˜˜ ÁÁ ¯Ë

2

˜ˆ˜ = 7. ˜˜ ¯

x= 14. Write in a+bi form:

−i + ( 7 − 5i) − 3 ( 2 − 3i)

15. Write in a+bi form:

( 3 − 2i)

2

3

1

2

3

4

12

16. Performance Task: Simplify i , i , i , i , . . . . i . Describe the pattern in the values for the powers of i.

The pattern is: 2

17. Solve by completing the square. −3x − 12x + 18 = 0

x= 2

18. Use the discriminant to determine the number of real solutions of the equation. 4x − 3x − 7 = 0 discriminant = number of real solutions is 19. Find the vertex by completing the square. Name the vertex. Check your answer using -b/(2a) 1 2 y = x − 2x + 10 2

vertex :

4

20. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t 2 seconds after it is thrown is given by d = − 16t − 4t + 412. How long after the rock is thrown is it 410 feet from the ground?

The rock is at 410 feet after 2

21. Consider the equation 4x − 6x + c = 0. 2

For what value of c does 4x − 6x + c = 0 have one real solution? Explain. 2

22. Graph y > − x + 1

2

23. Solve algebraically x + x − 72 < 0

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____ 24. Write an equation for the parabola shown.

a. b.

7 (x + 6 ) (x − 7 ) 36 ÁÊ 7 ˜ˆ˜˜ ÁÊÁÁ 1 y = −7 ÁÁÁÁ x + ˜ Áx − ÁË 36 ˜˜¯ ÁÁË 6 y=

c. ˜ˆ˜ ˜˜ ˜˜ ¯

d.

ÊÁ 1 ˆ˜ y = 5 ÁÁÁÁ x + ˜˜˜˜ ( x − 7 ) ÁË 6 ˜¯ 1 y = (x + 5 ) (x − 7 ) 6

25. Write a quadratic function in standard form for the parabola that passes through the points (–2, 27), (1, 6), and (2, 19).

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