Algebra 2 1st Nine Weeks Review
DO ALL WORK ON YOUR OWN PAPER FOR CREDIT!
1. How many solutions does the system of equations have? What is the solution to the system of equations?
2. Solve the system of equations by graphing.
(This is a multiple choice question justify with math)
a.
b.
c.
d.
3. Solve the system of equations by
substitution
4. When solving the following system of equations by elimination what will you multiply the second equation by to eliminate x? Justify your answer.
5. Solve the systems of equations.
6. Find the z-coordinate of the solution of the system.
7. A worker finds a ball on the roof of a building as he is doing some repairs. He tosses the ball up and off the roof so that its height above the ground is related to time after it has been tossed, by the function What was the maximum height reached by the ball?
8. A manufacturer determines that the number of drills it can sell is modeled by the equation , where p is the price of drills in dollars. At what price will the manufacturer sell the most number of drills? What is the maximum number of drills that can be sold?
9. Write the equation of the parabola in vertex form.
10. How does the parabola open. Find the vertex of the parabola, the maximum or minimum value, and the y-intercept. .
11. Use the graph of y = x² .If you translate the parabola to the right 2 units and down 7 units, what is the equation of the new parabola in vertex form?
12. State how the parabola opens. State the vertex and y-intercept:
13. How does the parabola open? What is the vertex and y-intercept of the graph ?
14. Solve the equation by factoring:
15. Solve the equation by factoring:
16. Solve the equation by factoring:
17. Factor:
18. Factor:
19. Factor:
20. Find the inverse of the function.
21. Find the inverse of the function.
22. Given a focus of (4, 3) and a directrix of
y = 1. Write the equation of the parabola given in vertex form.
23. What number must be added to both sides of the equation to complete the square?
24. Solve by completing the square:
25. Solve using the quadratic formula.
26. Solve:
27. Simplify:
28. Simplify:
29. Simplify:
30. Resort A charges $70 per night, plus a one-time surcharge of $5. Resort B charges $65 per night plus a one-time surcharge of $20. After how many nights will the total cost of the two options be the same?
a. Define the variables
b. Set up a system of equations to
solve the problem
c. Solve system of equations
by substitution or elimination.
d. What does the solution mean in
context of the word problem.
31. The graph of which system of inequalities is shown?
a. b.
c. d.
32. Write the explicit rule, find the 37th term, find the recursive rule.
33. Write the explicit rule, find the 6th term, find the recursive rule.
34. What is the sum of the arithmetic series?
35. Find the sum of the geometric series
36. Find the sum of the geometric series
37. Given the Quadratic equation:
a. Does the graph of this function have
maximum or minimum?
Justify your answer
b. Find the vertex algebraically.
c. What is the y-intercept?
d. Compare the width of the graph of this function to the width of the parent function. What causes this change?
38. Two points on the parabolic path of a catapulted smurf are (0,0) and vertex(24,12)
a. Using vertex form, create an equation that models the path of the smurf
b. At what coordinate (x, y) would the smurf land?
c. What does the y-coordinate of the vertex represent?
39. Given
a. Factor the function.
Write it in intercept form.
b. What are the x-intercepts
c. Using the x-intercepts.
What is the x-coordinate of the vertex?
d. What is the y-coordinate of vertex