No Calculators on This Section!

Algebra 2 Name ______Review 5.2-5.4

Graph the function FROM THE FORM IT IS IN – DO NOT FOIL! Label the vertex. Make a table with all 5 points.

NO CALCULATORS ON THIS SECTION!

1. Y = −3x2 + 5 2. f(x) = 2x2 – 8x + 6

3. y = −x2 + 8x – 12 4. f(x) = 3(x + 2)2 − 5

5. f(x) = ½(x – 3)2 + 4 6. Y = −(x – 5)2 + 6 Use the information given to write a quadratic equation in the form y = ax 2 + c .

7. 8. Through (0, 5) and (6, −4) 9. Through (2, −11) and (−3, −21)

Use the given information to write a quadratic equation in VERTEX FORM.

10. 11. Vertex: (4, −1) through (2, 11) 12. y = a(x + 3)2 + k through (1, −6) and (−1, 0)

Determine if the graph would have a maximum or minimum. Then find the vertex and y-intercept.

13. y = −3x2 + 18x – 7 14. y = 0.2(x + 7)2 + 3 15. Y = −x2 – 6

Write the function in standard form.

16. y = 3(x – 4)2 + 3 17. y = −½(x + 6)2 – 5

Write the function in vertex form.

18. y = −4x2 – 16x + 3 19. y = x2 – 2x 20. A manufacturer of lighting fixtures has daily production costs modeled by y = 0.25x2 – 10x + 800 where y is the total cost in dollars and x is the number of fixtures produced. How many fixtures should be produced each day to yield a minimum cost? What is the minimum daily production cost?

21. You are going to frame your family photo. You have 64 inches of framing materials.

a. What dimensions of the frame give you the maximum area for the photo?

b. Write an equation to represent this situation. Use your equation to justify your answer to part a.

22. The path a diver follows is given by y = −0.4(x – 4)2 + 14 where x is the horizontal distance (in feet) from the edge of the diving board and y is the height (in feet).

a. What is the maximum height of the diver?

b. What is the starting height of the diver? (when he or she is on the diving board)

c. Sketch a graph of the situation.

23. Researchers conducted an experiment to determine temperatures at which people feel comfortable. The percent y of test subjects who felt comfortable at temperature x (in degrees Fahrenheit) can be modeled by y = −3.678x2 + 527.3x – 18,807. What temperature made the greatest percent of test subjects comfortable? At that temperature, what percent felt comfortable?

24. The Golden Gate Bridge in San Francisco has two towers that rise 500 feet above the road and are connected 1 2 by suspension cables as shown. Each cable forms a parabola with equation y=( x -2100) + 8. 8960 a. What is the distance d between the two towers?

b. What is the height l above the road of a cable at its lowest point?

25. Suppose you are tossing an apple up to a friend on a third-story balcony. After t seconds, the height of the apple in feet is given by h = −16t2 + 38.4t + 0.96. Your friend catches the apple just as it reaches its highest point. What would the x-coordinate of the vertex tell us about this situation? What would the y-coordinate of the vertex tell us about this situation? BE SPECIFIC! Factor completely. WATCH OUT FOR GCFs!!

26. x2 − 9x + 14 27. m2 – 7m – 30 28. k2 + 13k + 36

29. 6x2 – 13x + 2 30. 10x2 – 3x – 1 31. 6x2 + 17x + 5

32. 2x2 – 4x – 30 33. −3x2 – 15x – 12 34. 6x2 – 33x + 15

35. x2 – 81 36. 25n2 – 36m2 37. 12p2 – 147

38. 25x2 – 20x + 4 39. −2x2 + 16x – 32 40. −15x2 + 10x