1. 7-1 EXPLORING QUADRATIC FUNCTIONS MISS BATTAGLIA – ALGEBRA 1 CP OBJECTIVE: GRAPH QUADRATIC FUNCTIONS OF THE FORM Y=AX^2

2. REAL WORLD APPLICATIONS - QUADRATICS Throwing a ball Bicycling up and down a hill Calculating Speed (Example: Avid kayakers, use quadratic equations to estimate their speed when going up and down a river)

3. WARM UP – WORK WITH A PARTNER

4. WHAT IS SYMMETRY? http://www.superteacherworksheets.com/geometry/symmetry-2_TZTDQ.pdf

5. QUADRATIC FUNCTIONS The graphs from the warm up are all parabolas. If you draw a parabola on a piece of paper, you can fold the paper down the middle of the parabola and the two sides will match exactly. The line down the middle of the parabola is the axis of symmetry.

6. DRAW THE AXIS OF SYMMETRY

7. QUADRATIC FUNCTION

8. EXAMPLE

9. MAKE A TABLE OF VALUES & GRAPH THE QUADRATIC FUNCTIONS x2x 2 -2x 2 -2 0 1 2

10. The highest or lowest point on a parabola is called the vertex of the parabola. When a parabola opens upward, the y-coordinate of the vertex is the minimum value of the function. When a parabola opens downward, the y-coordinate of the vertex is the maximum value of the function.

11. EXAMPLE

12. USE A GRAPHING CALCULATOR

13. EXAMPLE Order each group of quadratic functions from widest to narrowest graph. y = 2x 2, y = 3x 2, y = -5x 2

14. HOMEWORK Pg 321 # 2 – 4, 6, 7, 9, 11, 12