Algebra 2 Chapter 5 test 2
Name____________________________
1.
Using the equation, y = x2 – 10x + 26,
a) State the vertex of the parabola.
b) Write the equation of the line of symmetry.
c) Graph the parabola. On graph # 1
2.
Using the equation, y = -x2 – 2x + 6,
a) State the vertex of the parabola.
b) Write the equation of the line of symmetry.
c) Graph the parabola. On graph # 2
3.
Graph the inequality, y  x2 + 6x + 13, on graph # 3
4. Use the discriminant to determine the number of real solutions to the equation 3x2 + 8x - 3 = 0.
In 5 – 12, solve the equations, write imaginary answers in standard a + bi, form.
5. 2x2 – 3x – 5 = 0
6. 3x2 = 12
7. 2x2 + 2x - 7 = 0
8. x2 + 2x – 1 = 3x2 + 8
9. x2 + 4x + 7 = 0
10. 4x2 - 5x – 1 =-5x + 16
11. 6x2 + 11x = 35
12. x2 = 4x + 1
13. Decide whether 1 – 3i, is a solution of x2 – 2x + 5 = 0, show work to justify answer.
14. Graph and label each on the Complex plane on graph # 4.
a) 3 – 4i
b) 5i
c) – 3 + i
In 15 – 17, simplify each of the following expressions.
15. (3 + 9i) + (4 – 3i)
16. -3i(-2 + 5i)
17. (4 – 2i)(4 + 3i)
18. For 1983 to 1993, the number, b (in millions), of recreational boats owned in the United States
can be approximated by the model, b = -.01t2 + .59t + 11.28, where t = 3 represents 1983. I what
year were 15.8 million recreational boats owned?
19. What is the initial velocity necessary for a person who can reach 95” to jump in order to be able
to dunk a basketball at a 10’ hoop?
20. A boat is an unknown distance due east of a second boat. After a time the first boat has traveled
7km further east while the second has traveled 7 km due north. At that time the boats are 25
km apart, how far apart did the boats begin?
25 km
7 km
x km
7 km
Extra Credit, solve the equation by completing the square. Show work to demonstrate method used.
E1. x2 – 12x + 8 = 0
E2. 3x2 + 6x – 3 = 0
E3. 2x2 + 6x – 7 = 0