Unit Five Quadratic Functions

Algebra II Practice Test Unit Five – Quadratic Functions

Name______Period_____Date______

NON-CALCULATOR SECTION

Vocabulary: Define each word and give an example.

1. Quadratic Function

2. Zero (of a function)

3. Complex Number

Short Answer:

4. Describe how to find the absolute value of a complex number. Show graphically how the formula is derived.

5. What is the discriminant of the quadratic equation ax2 + bx + c = 0 ? Describe what it means if the discriminant is negative, positive, or zero.

Review: 轾4- 3 6. Find the inverse of the matrix: 犏臌2- 5

7. Write an equation in standard form for the line perpendicular to -3x + 2 y = - 5 that passes through the point (2,- 1) .

2 8. Find f (-2) for f( x) =2 x - 3 x + 1

Problems: **Be sure to show all work used to obtain your answer. Circle or box in the final answer.** 9. Simplify: 4 108 20 a. b. - c. 225- - 49 9 7

of 7 10. Graph the quadratic functions. Label the vertex and axis of symmetry on each graph. 2 a. y= - x2 +1 b. y=( x -2) + 4 c. y= x2 -2 x - 5

11. Solve the quadratic equations by factoring.

a. 4x2 - 25 = 0 b. -9x2 + 12 x - 4 = 0 c. 6 =x2 - x

12. Solve the quadratic equations by square roots.

2 a. 5x2 = 100 b. 3( x + 1) + 4 = 22 c. -2x2 = 6

13. Solve the quadratic equation by completing the square: 2x2 - 4 x + 20 = 0

14. Solve the quadratic equation by the quadratic formula: 4x2 + 2 x = 5

of 7 15. Simplify the following: 2 3- i a. (-5 - 8i) -( - 4 - 7 i) b. (3+ 2i) c. 2+ 5i

16. Write y= x2 +8 x - 9 in vertex form. Find the zeros and the vertex of the function.

17. Solve the quadratic inequalities: a. 9x2 - 16 < 0 b. x2 - 3 x � 10

18. Graph the quadratic inequalities: a. y< x2 -4 x + 3 b. y� x2 4 x

of 7 Multiple Choice Questions: Circle the best answer.

2 19. Which graph represents the function y= -4( x + 8 x + 15) ? y y A. 10 B. 10

-10 -5 5 10 x -10 -5 5 10 x

-10 -10

y y 10 10 C. D.

-10 -5 5 10 x -10 -5 5 10 x

-10 -10

20. What are the solutions of the quadratic equation 3x2 + 5 x = - 4 ?

-5 +i 23 - 5 - i 23 A. x = , 6 6 -5 +i 73 - 5 - i 73 B. x = , 6 6 5+i 23 5 - i 23 C. x = , 6 6 5+i 73 5 - i 73 D. x = , 6 6

21. Which is one of the appropriate steps in finding the solutions for x2 +8 x - 9 = 0 when solved by completing the square?

2 A. (x +4) = 25 2 B. (x +4) = 9 2 C. (x +8) = 9 D. (x+9)( x - 1) = 0

of 7 2 - i 22. Write the expression as a complex number in standard form. 3- 2i

2 1 A. - i 3 2 2 1 B. + i 3 2 8 7 C. - i 13 13 8 1 D. + i 13 13

2 23. For the scenario below, use the model h= -16 t + v0 t + h 0 , where h = height (in feet), h0 = initial height (in feet), v0 = initial velocity (in feet per second), and t = time (in seconds).

A cheerleading squad performs a stunt called a “basket toss” where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward, leaving her teammates’ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second.

When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air?

1 A. second 16 B. 1 second 9 C. 1 second 16 D. 2 seconds

of 7 Algebra II Practice Test Unit Five – Quadratic Functions

Name______Period_____Date______

CALCULATOR SECTION

1. Old Faithful in Yellowstone Park is probably the world’s most famous geyser. Old Faithful sends a stream of boiling water into the air. During the eruption, the height h (in feet) of the water t seconds after being forced out of the ground could be modeled by h= -16 t2 + 150 t .

a. What is the initial velocity of the boiling water?

b. What is the maximum height of the boiling water?

c. How long is the boiling water in the air?

2. From 1970 to 1990, the average cost of a new car, C (in dollars), can be approximated by the model C=30.5 t 2 + 4192 , where t is the number of years since 1970. During which year was the average cost of a new car $12,000?

3. A punter kicked a 41-yard punt. The path of the football can be modeled by y= -0.035 x2 + 1.4 x + 1 , where x is the distance (in yards) the football is kicked and y is the height (in yards) the football is kicked. Find the maximum height of the football.

of 7 4. Solve the quadratic equation ax2 + bx + c = 0 by completing the square.