1. Graphing Quadratic Functions A quadratic function is an equation of the form: y = ax 2 + bx + c

2. How long does a firework stay in the air?

3. What is the hang time of a football?

4. How does a satellite dish work?

6. The graph of a quadratic function is called a parabola. It looks like a U or an upside down U.

7. Gallileo was the first to show that the path of an object thrown in space is a parabola.

8. Graphing A Parabola xy = x 2 – 2x – 3y -2 0 1 2 3 4 To graph a parabola we create a table of values and then plot the points. Lets Graph: y = x 2 – 2x – 3

9. y = x 2 – 2x – 3 xy -25 0 0-3 1-4 2-3 30 45

10. Graphing A Parabola Lets Graph: y = -x 2 + 2x + 1 xy = -x 2 + 2x + 1y -2 0 1 2 3 4

11. y = -x 2 + 2x +1 xy -2-7 -2 01 12 21 3 4-7 y = -x 2 + 2x + 1

12. Vertex (Turning Point) Quadratic Equation: y = ax 2 + bx + c  The maximum or minimum point is called the vertex or turning point of the parabola.  If a is positive the graph looks like a smile. (Minimum)  If a is negative the graph looks like a frown. (Maximum)

13. Axis of Symmetry  The line that divides a parabola directly in half is called its axis of symmetry.  The axis of symmetry and vertex (turning point) can be found using the equation:

14. Golden Gate Bridge The cables that act as suspension are parabolas.

15. 3) y = -x 2 + 4x – 1 Vertex is at: y = -x 2 + 4x – 1 xy y = ax 2 + bx + c

16. y = -x 2 + 4x – 1 xy -6 0 12 23 32 4 5-6 Vertex? Max or Min? Axis of Symmetry?

18. 4) y = x 2 – 2x – 8 Vertex is at: y = x 2 – 2x – 8 xy y = ax 2 + bx + c

19. y = x 2 – 2x – 8 xy -20 -5 0-8 1-9 2-8 3-5 40 Vertex? Max or Min? Axis of Symmetry?

20. Homework Graphing Parabolas Homework #1