Midterm Review
Unit 1: Polynomials
1. Factor the following polynomials.
a.)x2 -16b.) x2 +9x +14c.) 3x2 +18x+27
d.) 8x2 +2x -3e.) 27a3- 8b3f.)x2-5x-6
2. If f(x)=(x+6)(3x-9) what are the zeros of the function?
3. Rewrite the expression in the form bn where n is a rational exponent.
a. b.
4. Use the quadratic formula to find the zeros of the following polynomial expression
f(x)=x2+x-4
Unit 2: Rational and Radical Expressions
5. What is i37 equivalent to?6. Simplify (2+3i)(4-i)
7. Simplify the rational expressions
a. b.
8. Solve for x
a. 5 =b. 2x4 =512
9. Consider the following polynomial y=4x3-2x2+x-7
- Divide the given polynomial by (x-2) using synthetic division.
- Is (x+5) a factor of the given polynomial?
Unit 3: Functions
Inverse
10. Find the inverse of the function: f(x) = 2x3+3
11. In the graph on the right, are the two quadratic functions inverse of each other?
Describing Polynomials
12. For the polynomial f(x)=3x6+4x3-2x +3 describe f(x) when x approaches ∞
13. What is the multiplicity of x = -2 and x = -4?
14. Using the graph on the right.
a. Write an equation for the function given the graph using zeros and their multiplicities
b. Describe the end behavior for the following graph
Even, Odd, Neither
15. Is the following function even, odd or neither?
a. f(x) = -3x2 +4b.
Function Notation
16. Use the graph to find the value of x when f(x)=10
17. Use the given functions f(x)=x2-5x+2 and g(x)=2(x-1)2+3
- f(-2)b. f(1)-g(-2)
18. Jose kicks a football into the air. The function h(t) = -16t2+40t can be used to determine the height in feet, h, of the ball after t seconds. What will be the height of the ball after 2 seconds?
Transformations
19. Given the function below, answer the following questions.
y = 2Ix-4I+7
- Name the parent function
- Describe how the graph of the function compares with that parent function.
20. Make an accurate sketch of the graph of the given equation
y=(x+2)2-4
21. Write a transformation equation for the graph below
Unit 4: System of Equations
22. A cab company offers two monthly prices. The yellow cab charges $1.80 per mile plus a $2.00 fee. The blue cab charges $0.90 per mile and a $5.00 fee. What is the minimum number of miles you could travel in order for the blue cab to be the less expensive option?
23. You have two job offers for summer. One job offers $12 an hour. The second job offers $100 for starting the job then $9.50 a week. How many hours would you have to work to get paid the same at both jobs?
24. Solve the following system of equation. Enter the solutions as ordered (x,y).
y=4x+7 and y=x2-5
25. Solve the following system of equations by using matrices on your calculator.
-x-5y-5z = 2
4x-5y+4z = 19
x+5y-z = -20