1. Quadratic Functions Copyright 2014 Scott Storla

3. Quadratic Functions Vocabulary Copyright 2014 Scott Storla

4. The graph of a quadratic function is called a parabola. Copyright 2014 Scott Storla

5. This parabola “opens up” Copyright 2014 Scott Storla

6. This parabola “opens down”. Copyright 2014 Scott Storla

7. The vertex is the “turning point” of the parabola. Copyright 2014 Scott Storla

8. When a parabola opens up the value of the y-coordinate of the vertex is the “minimum”. Copyright 2014 Scott Storla

9. When a parabola opens down the value of the y-coordinate of the vertex is the “maximum”. Copyright 2014 Scott Storla

10. The axis of symmetry is a line parallel to the y- axis that divides the parabola into two halves which are “mirror images”. Copyright 2014 Scott Storla

11. The y-intercept is the point that the graph and the y-axis share. Copyright 2014 Scott Storla

12. The x-intercept(s) are any points that the graph and the x-axis share. Copyright 2014 Scott Storla

13. The x-intercept(s) are any points that the graph and the x-axis share. Copyright 2014 Scott Storla

14. The x-intercept(s) are any points that the graph and the x-axis share. Copyright 2014 Scott Storla

15. Discuss whether the graph opens up or down, the vertex, any minimum or maximum, the axis of symmetry and any intercepts. Opens down Vertex (0,6) Maximum of 6 Axis of symmetry x = 0 y-intercept (0,6) x-intercepts (-2,0) (2,0) Copyright 2014 Scott Storla

16. Discuss whether the graph opens up or down, the vertex, any minimum or maximum, the axis of symmetry and any intercepts. Opens up Vertex (2,-2) Minimum of -2 Axis of symmetry x = 2 y-intercept (0,0) x-intercepts (0,0) (4,0) Copyright 2014 Scott Storla

17. Opens up Vertex (-6,0) Minimum of 0 Axis of symmetry x = -6 y-intercept (0,9) x-intercept (-6,0) Discuss whether the graph opens up or down, the vertex, any minimum or maximum, the axis of symmetry and any intercepts. Copyright 2014 Scott Storla

18. Opens down Vertex (-4,-4) Maximum of -4 Axis of symmetry x = -4 y-intercept (0,-8) x-intercepts none Discuss whether the graph opens up or down, the vertex, any minimum or maximum, the axis of symmetry and any intercepts. Copyright 2014 Scott Storla

19. Quadratic Functions Vocabulary Copyright 2014 Scott Storla

20. Quadratic Functions Graphing Standard Form Copyright 2014 Scott Storla

21. Graphing a Parabola written in Standard Form Copyright 2014 Scott Storla

22. Opens up y-intercept (0,7) Vertex (4,-9) Axis of symmetry x = 4 x-intercepts (1,0) (7,0) Copyright 2014 Scott Storla

23. Opens down y-intercept (0,8) Vertex (-1,9) Axis of symmetry x = -1 x-intercepts (-4,0) (2,0) Copyright 2014 Scott Storla

24. Opens up y-intercept (0,14) Vertex (-3,-4) Axis of symmetry x = -3 x-intercepts (-4.4,0) (-1.6,0) Copyright 2014 Scott Storla

25. Opens up y-intercept (0,25) Vertex (3,-2) Axis of symmetry x = 3 x-intercepts (2.2,0) (3.8,0) Copyright 2014 Scott Storla

26. Quadratic Functions Graphing Standard Form Copyright 2014 Scott Storla

27. Graphing a Parabola written in Standard Form Copyright 2014 Scott Storla

31. Discuss the meaning of R(0) both in English and Algebraically. Discuss the meaning of R(t) = 43.5 both in English and Algebraically. Translate, “Find the amount recovered in 1997” into functional notation and use the function to answer the question. Translate, “In what year does the amount recovered first reach 50 million tons?” into functional notation and use the function to answer the question.

32. Copyright 2014 Scott Storla What does the coefficient –0.1 imply about future growth? Find the year the number of subscribers will peak. Find how many subscribers there will be during the peak year. Graph the function. (Make sure you label and scale your axes.) Predict when the number of subscribers will again reach the 1995 level.

33. Copyright 2014 Scott Storla What does the coefficient imply. Find the vertex and discuss the meaning of both coordinates. Ask, "When will there be 2,000,000 farms?" using functional notation and use the function to answer the question. Find F(37) and discuss its meaning. Find the number of farms 20 years after there were 2,400,000 farms.

34. 1. Do you expect the shape of the graph to be opening up or down? What does this say about the height of the ball? 2. After how many seconds will the ball reach its maximum height? 3. How high will the ball get? 4. How long before the ball hits the ground? 5. After how many seconds will the ball be 120 feet above the ground? Copyright 2014 Scott Storla

35. 1. What is T(-1) asking? 2. Find T(-1)? 3. Ask the question, “How many lung transplants do you expect this year?” using functional notation. 5. Ask the question, “What is the first year the number of transplants will reach 1,200?” using functional notation. 4. Answer the question posed in question 3. 6. If T(t) = 1,200, what’s t? Copyright 2014 Scott Storla