Algebra 2 SOL Packet #2 Topics: Functions through Quadratics

Name:
SOL Packet #2
Topics: Functions through Quadratics
Show all work in order to receive full credit!!
Algebra 2
1. The graph of y = 4 x −11 is translated up 8 units. Which equation represents the
translated graph?
a. y = 4 x −19
b. y = 12x − 3
€
c. y = 12x −11
d. y = 4 x − 3
€
€
€
2. Indicate the intervals where the graph of f (x) = (x +1) 2 (x −1) 2 is decreasing throughout
€
the interval. (Hint: Graph the function using a calculator first!)
€
3. Shade the correct area: y ≤ −x + 3
€
1 4. Shade the region that represents the solution to the inequality: y > x + 4 −1
€
5. What is the factored form of x 2 − 36z 2 ?
a. (x + 6z)(x − 6z)
b. (x + z)(x − 36z)
c. (x + 6z) 2 €
d. (x − 6z) 2
€
€
6.€ Which of these is equivalent to 1?
€
a. i 24
b. i 42
c. i 66
d. i 82
€
€
7.€ Which complex number is equivalent to: (7 − 9i) − (−1+ 3i) ?
€
a. 6 − 6i
b. 6 −12i
c. 8 − 6i
€
d. 8 −12i
€
€
€
8. Which is equivalent to 13 − −81 ?
€
a. 4
b. 13 − 9i
c. 13 + 9i€
d. 22
€
€
2 9. What is the solution set of the equation: x 2 − 2x + 5 = 0 ?
a. {-3, 1}
b. {-1, 3}
c. {1 − 2i, 1+ 2i}
€
d.
{−1 − 2i, −1+ 2i}
€
10. Which is the solution set for (x + 5) 2 = 0 ?
€
a. 25
b. 5
c. -5
€
d. -5 and 5
11. What is the solution set of 2x 2 + 7x + 5 = 0 ?
⎧
1 ⎫
a. ⎨ −5, − ⎬
⎩
2 ⎭
⎧ 5
⎫€
b. ⎨ − , −1⎬
⎩ 2
⎭
⎧ 5 ⎫
€
c. ⎨1, ⎬
⎩ 2 ⎭
⎧ 1 ⎫
€
d. ⎨ , 5 ⎬
⎩ 2 ⎭
€
12. Which graph most likely represents a function with a zero of 5?
€
3 13. What are the coordinates of the vertex of the graph of the function: −2(x −1) 2 = y + 5 ?
(Hint: How can you rewrite this equation to be in vertex form?)
a. (-1, 5)
b. (2, 5)
€
c. (1, -5)
d. (-2, -5)
14. Where does the graph of f (x) = (3x − 5)(x + 9) cross the x-axis?
⎛ 5 ⎞
a. ⎜ , 0⎟ and ( −9,0)
⎝ 3 ⎠
⎛ 5 ⎞ €
b. ⎜ , 0⎟ and ( −3,0)
⎝ 3 ⎠
⎛ 5 ⎞
€
c. ⎜ − , 0⎟ and (9,0)
⎝ 3 ⎠
⎛ 5 ⎞
€
d. ⎜ − , 0⎟ and ( −45,0)
⎝ 3 ⎠
€
15. Identify which of the following are factors of this polynomial: 18x 2 +120x +150
€
6 3x+5 3x-­‐5 X+1 2 €
x+5 4