2. What information can we visually determine from this Quadratic Graph? Vertex Vertical Stretch Factor (4, -3) Over 1, up 1 Over 2, up 4 Normal Pattern so VS=1 So the function is

3. What information can we visually determine from this Quadratic Graph? Vertex Vertical Stretch Factor (-2, 1) Over 1, up ? Over 2, up ? Over 3, up 3 ( ) so VS= So the function is

4. What about this Quadratic Graph? Vertex Vertical Stretch Factor (1, -5) Over 1, down 2 Over 2, down 8 so VS= -2 So the function is

5. Now it’s your turn! Determine the Functions that model each of these curves: Curve B Curve A

6. Determine the Functions that model each of these curves: Curve B Curve A 2 Sad Parabolas Why? a < 1

7. Determine the Functions that model each of these curves: Curve B Curve A 2 Happy Parabolas Why? a > 1

8. Remember, quadratic functions represent real-life situations such as: Real Life Connection …the height of a kicked soccer ball y = (-9.8)t 2 + 20t …the motion of falling objects pulled by gravity: height = -16t 2 + 100

9. Graphs of Quadratic Functions Quadratic Functions graph into a shape called a Parabola If the vertical stretch, “a”, is negative, the parabola opens downward If the vertical stretch, “a”, is positive, the parabola opens upward Vertex Maximum Point Minimum Point

10. Determining Functions of Parabolas ALGEBRAICALLY! 1. Find the equation of the parabola having a vertex of (3, 5) passing through the point (1, 2). SUBSTITUTE The FUNCTION for this parabola is:

11. Determining Functions of Parabolas ALGEBRAICALLY! 2. Find the equation of the parabola having a vertex of (-1, 4) with a y-intercept of –3. SUBSTITUTE The FUNCTION for this parabola is:

12. Determining Functions of Parabolas ALGEBRAICALLY! 3. A quadratic function has x-intercepts (-1, 0) and (5, 0). Find the formula for the function if it has a maximum value of 6. SUBSTITUTEThe FUNCTION for this parabola is: The axis of symmetry is located halfway between the two intercepts so x=2 is the axis of symmetry.

13. Determining Functions of Parabolas ALGEBRAICALLY! 4. A bridge is shaped as a parabolic arch. If the maximum height is 20 m and the bridge spans 60 m, find the function that models this situation. The FUNCTION for this model is: 20 m 60 m

15. Homework: Page 38 #39. 42, 43, 44