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Unit 12 Review
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1. Simplify a. ๐ b. โ ๐ 51
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1. Simplify a. ๐ b. โ ๐ 51
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2. Simplify a. 5โ2๐ 3๐ b. 5โ2๐ 2+5๐
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2. Simplify a. 5โ2๐ 3๐ b. 5โ2๐ 2+5๐
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3. Simplify a. (3-2i)(4+2i) b. (3-2i)-4(4-2i)
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3. Simplify a. (3-2i)(4+2i) b. (3-2i)-4(4-2i)
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4. Find all the solutions for ๐ฅ by the method of your choice. a
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4. Find all the solutions for ๐ฅ by the method of your choice. a
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5. Find all the solutions for ๐ฅ by the method of your choice. a
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5. Find all the solutions for ๐ฅ by the method of your choice. a
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6. Find all the solutions for ๐ฅ by the method of your choice. a
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6. Find all the solutions for ๐ฅ by the method of your choice. a
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7. Find all the solutions for ๐ฅ by the method of your choice. a
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7. Find all the solutions for ๐ฅ by the method of your choice. a
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8. Find all the solutions for ๐ฅ by the method of your choice. a
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8. Find all the solutions for ๐ฅ by the method of your choice. a
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9. Find all the solutions for ๐ฅ by the method of your choice. a
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9. Find all the solutions for ๐ฅ by the method of your choice. a
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10. An arrow is shot into the air so that its height can be found by the formula โ ๐ก =112โ2๐กโ2 ๐ก 2 . A) Find the maximum height. B) When does the arrow hit the ground?
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10. An arrow is shot into the air so that its height can be found by the formula โ ๐ก =112โ2๐กโ2 ๐ก 2 . A) Find the maximum height. B) When does the arrow hit the ground?
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11. Find the equation of the parabola in vertex form.
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11. Find the equation of the parabola in vertex form.
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12. Find the following for ๐ ๐ฅ =โ ๐ฅ 2 +6๐ฅโ8. a
12. Find the following for ๐ ๐ฅ =โ ๐ฅ 2 +6๐ฅโ8. a. The x-intercepts of ๐(๐ฅ). b. Where ๐(๐ฅ) decreasing? c. The axis of symmetry d. The maximum value
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12. Find the following for ๐ ๐ฅ =โ ๐ฅ 2 +6๐ฅโ8. a
12. Find the following for ๐ ๐ฅ =โ ๐ฅ 2 +6๐ฅโ8. a. The x-intercepts of ๐(๐ฅ). b. Where ๐(๐ฅ) decreasing? c. The axis of symmetry d. The maximum value
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13. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is narrower than ๐(๐ฅ).
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13. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is narrower than ๐(๐ฅ).
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14. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is wider than ๐(๐ฅ).
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14. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is wider than ๐(๐ฅ).
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15. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is a reflection of ๐(๐ฅ).
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15. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation with the same vertex that is a reflection of ๐(๐ฅ).
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15. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation that is a translation of ๐(๐ฅ) three units left and 5 units up.
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15. Given the equation ๐ ๐ฅ =4 ๐ฅ , write an equation that is a translation of ๐(๐ฅ) three units left and 5 units up.
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16. Identify the zeros of the function ๐ ๐ฅ = ๐ฅ 2 โ5๐ฅโ24.
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16. Identify the zeros of the function ๐ ๐ฅ = ๐ฅ 2 โ5๐ฅโ24.
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17. The height of a ball is modeled by the equation โ ๐ก =โ256 ๐ฅโ Find the time it takes the ball to reach its maximum height.
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17. The height of a ball is modeled by the equation โ ๐ก =โ256 ๐ฅโ Find the time it takes the ball to reach its maximum height.
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18. The path of a cannon ball is modeled by the graph.
What is the domain and range of the model?
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18. The path of a cannon ball is modeled by the graph.
What is the domain and range of the model?
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19. The path of a cannon ball is modeled by the graph.
How long did the cannon stay in the air?
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19. The path of a cannon ball is modeled by the graph.
How long did the cannon stay in the air?
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20. Simplify the following: a) โ23 b) โ52 c) โ64 d) ๐โ
๐โ
๐โ
๐โ
๐โ
๐โ
๐
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20. Simplify the following: a) โ23 b) โ52 c) โ64 d) ๐โ
๐โ
๐โ
๐โ
๐โ
๐โ
๐
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21. ๐ ๐ฅ = ๐ฅ 2 โ12๐ฅ+35 a) Vertex b) x-intercepts c) y-intercept d) max/min value
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21. ๐ ๐ฅ = ๐ฅ 2 โ12๐ฅ+35 a) Vertex b) x-intercepts c) y-intercept d) max/min value
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22. ๐ ๐ฅ = 2 3 ๐ฅ+5 2 โ7 a) Line of symmetry b) vertex c) domain d) range
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22. ๐ ๐ฅ = 2 3 ๐ฅ+5 2 โ7 a) Line of symmetry b) vertex c) domain d) range
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23. Find the value of ๐ that makes the expression a perfect square trinomial: ๐ฅ 2 โ15๐ฅ+๐
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23. Find the value of ๐ that makes the expression a perfect square trinomial: ๐ฅ 2 โ15๐ฅ+๐
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24. Write the quadratic function ๐ฆ=4 ๐ฅ 2 +16๐ฅ+7 in vertex form by completing the square. Then identify the vertex.
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24. Write the quadratic function ๐ฆ=4 ๐ฅ 2 +16๐ฅ+7 in vertex form by completing the square. Then identify the vertex.
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25. Which has a greater minimum value?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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25. Which has a greater minimum value?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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26. Which has a smaller x-value at the minimum?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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26. Which has a smaller x-value at the minimum?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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27. What is the product of the x-intercepts of ๐ ๐ฅ ?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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27. What is the product of the x-intercepts of ๐ ๐ฅ ?
Statement True False 8a. The minimum value of ๐(๐ฅ) is greater than the minimum value of ๐(๐ฅ). 8b. The value of ๐ฅ when ๐(๐ฅ) is at its minimum is less than the value of ๐ฅ when ๐(๐ฅ) is at its minimum. 8c. Both ๐ฅ intercepts of ๐ ๐ฅ occur when ๐ฅ is greater than zero. 8d. The line of symmetry of ๐(๐ฅ) is ๐ฅ=1.
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