Review Problems, Maximizing Volume (Must do 300 before 400) and Pattern Designs
Writing Quadratic Functions and Tranformations
Using your calculator to find Quadratic Regressions, imaginary numbers and Degrees and Zeros
The discriminant and the Quadratic Formula
Even and Odd Degree Functions, Translations of Graphs bigger than Quadratics, Zeros
100
Review Problems: Perform each indicated operation. State whether the expression in your answer is linear, quadratic, cubic, or exponential. 1. (4x + 7) + (3x – 5) 2. (2x – 3)(5x + 4)
1. 7x + 2 Linear 2. 10x^2 - 7x - 12 Quadratic
100
7. Given the function f(x)=-3x^2+6x+1 find the following: a) The concavity of the function (up or down). b) The y-intercept.
a. Down b. (0, 1)
100
14. Use your graphing calculator to find a quadratic function that passes through the points (-3, -37), (0, -4), and (3, -7).
14. f(x) = -2x^2 + 5x - 4
100
19. What is the discriminant of a quadratic equation? What does the value of the discriminant tell you about the number and type of solutions of a quadratic equation?
Discriminant is b^2 - 4ac positive means 2 real solutions zero means 1 real solution (a double root) negative means 2 imaginary solutions
100
26. Explain how even-degree functions and odd-degree functions differ in terms of their end behavior. 27. Label each graph below as odd-degree or even-degree.
26. Odd Degree = one end goes to negative infinity and one goes to positive infinity Even Degree = both ends end the same way 27. a. Odd b. Even c. Odd
200
Review Problems: Perform each indicated operation. State whether the expression in your answer is linear, quadratic, cubic, or exponential. 3. 3(x – 2)(x – 6) 4. 6x(x2 – 7)
3. 3x^2 - 24x + 36 Quadratic 4. 6x^3 - 42x Cubic
200
8. Given the function f(x)=(x + 5)(x – 2), find the following: a) The concavity of the function. b) The x-intercepts. c) The y-intercept (Hint: rewrite in standard form).
a. Up b. (-5, 0) and (2, 0) c. (0, -10)
200
15. A soccer ball that is kicked from the ground by a goalie is at a height of 20 feet after it has traveled 30 feet from the goalie, and the ball lands 150 feet away from the goalie. Write a quadratic function that represents the height of the soccer ball in terms of its distance from the goalie.
15. f(x) = -.006x^2 + 0.83x + 0
200
Solve each equation using the Quadratic Formula. Simplify each answer completely. 20. x^2 + 5x – 6 = 0
x = 1 and x = -6
200
Describe each translation of f(x). 28. f(x) = x^3; g(x) = -x^3 + 6 29. f(x) = x^4; g(x) = (x + 5)^4 – 2
28. Reflection over x-axis, Up 6 29. Left 5, Down 2
300
5. Complete the table. Include and expression for volume. Height Width Length Volume 0 1 1.5 2 3 4 h
5. Complete the table. Include and expression for volume. Height Width Length Volume 0 10 14 0 1 8 12 96 1.5 7 11 115.5 2 6 10 120 3 4 8 96 4 2 6 48 h (10-2h) (14 - 2h) V(h)=h(10-2h)(14-2h)
300
9. Given the function f(x)=-(x – 4)^2 + 3, find the following: a) The concavity of the function. b) The vertex. c) The y-intercept.
a. Down b. (4, 3) c. (0, -13)
300
16. A batter hits a baseball when it is 3 feet off the ground. When the ball is 150 feet away, it reaches its maximum height of 90 feet. When the ball is 300 feet away, it is 3 feet off the ground. Write a quadratic function that represents the height of the baseball in terms of its distance from the batter.
16. f(x) = -.004x^2 + 1.16x + 3
300
Solve each equation using the Quadratic Formula. Simplify each answer completely. 21. 3x^2 – 6x + 15 = 0
x = 1 + 2i and x = 1 - 2i
300
31. Find the zeros of the function f(x) = (x – 2)(x + 7)^2 32. Find the x-intercepts of the function f(x) = (x + 1)^2(x – 8)^3
31. (2,0) and (-7, 0) and (-7, 0) {(-7,0) is Multiplicity 2} 32. (-1, 0) and (-1, 0) and (8, 0) and (8, 0) and (8,0) {(-1, 0) is Multiplicity 2 and (8, 0) is Multiplicity 3}
400
What dimensions of the box give the maximum volume? What is the maximum volume?
Height = 1.92 Width = 6.16 Length = 10.16 Volume = 120.16
400
Look at Question 10 and 11 from your review packet. Circle the letter of the function that represents each graph.
10. B 11. C
400
17. What is the square root of -36? 18. (7 - 2i) (3 + 4i)
17. plus or minus 6i 18. 29 + 22i
400
Solve each equation using the Quadratic Formula. Simplify each answer completely. 22. 4x^2 + 20x + 25 = 0
x = -2.5 (it's a double root)
400
33. Given a function f(x) = (x+2)(x-5)(2x-1) a. Find the zeros of the function.
a. (-2, 0) and (5, 0) and (1/2, 0)
500
6. Use the tile designs below to answer the following questions. a. Draw Design 4. b. How many tiles will be in Design 5? c. Write two expressions that represent the total number of tiles in Design n. d. How many tiles will be in Design 8?
a. Draw on board b. 40 c. n^2 + 2n + n or n^2 + 3n or n(n+3) or anything that will give you the correct number of titles d. 88
500
Describe each transformation: 12. f(x+5) - 4 13. -f(x-2)
12. Down 4, Left 5 13. Reflected over x-axis (concave down), Right 2
500
24. Explain the relationship between the degree of a function and number of zeros of a function. 25. Sketch and example of: a. Two real zeros b. Two imaginary zeros c. A double root
24. The degree number is the same as the number of zeros. 25. Draw on board
500
Solve each equation using the Quadratic Formula. Simplify each answer completely. 23. 0 = -x^2 – 2x – 10
x = -1 + 3i and x = -1 - 3i
500
33. Given a function f(x) = (x+2)(x-5)(2x-1) b. Write the function in standard form.
b. f(x) = 2x^3 - 7x^2 - 17x + 10
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