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SOL Packet #2
Topics: Functions through Quadratics
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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
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c. y = 12x −11
d. y = 4 x − 3
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2. Indicate the intervals where the graph of f (x) = (x +1) 2 (x −1) 2 is decreasing throughout
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the interval. (Hint: Graph the function using a calculator first!)
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3. Shade the correct area: y ≤ −x + 3
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1 4. Shade the region that represents the solution to the inequality: y > x + 4 −1
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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
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6.€ Which of these is equivalent to 1?
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a. i 24
b. i 42
c. i 66
d. i 82
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7.€ Which complex number is equivalent to: (7 − 9i) − (−1+ 3i) ?
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a. 6 − 6i
b. 6 −12i
c. 8 − 6i
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d. 8 −12i
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8. Which is equivalent to 13 − −81 ?
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a. 4
b. 13 − 9i
c. 13 + 9i€
d. 22
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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}
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d.
{−1 − 2i, −1+ 2i}
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10. Which is the solution set for (x + 5) 2 = 0 ?
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a. 25
b. 5
c. -5
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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 ⎫
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c. ⎨1, ⎬
⎩ 2 ⎭
⎧ 1 ⎫
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d. ⎨ , 5 ⎬
⎩ 2 ⎭
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12. Which graph most likely represents a function with a zero of 5?
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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)
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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 ⎞
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c. ⎜ − , 0⎟ and (9,0)
⎝ 3 ⎠
⎛ 5 ⎞
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d. ⎜ − , 0⎟ and ( −45,0)
⎝ 3 ⎠
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15. Identify which of the following are factors of this polynomial: 18x 2 +120x +150
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6 3x+5 3x-­‐5 X+1 2 €
x+5 4