1. Graphs of Quadratic Equations

2. Standard Form: y = ax 2 +bx+ c Shape: Parabola Vertex: high or low point

3. Axis of Symmetry: Line that divides parabola into two parts that are mirror image of each other. Axis of Symmetry Vertex

4. The vertex has an x-coordinate of The axis of symmetry is the vertical line passing through

5. y = x 2 First find the vertex. This is the x value of the vertex, now find the y value. If x = 0, y = 0 Vertex = (0,0) 0 is the axis of symmetry:

6. Example: y = x 2 Make a table for y = x 2 Since the vertex is (0,0), pick an x value to the right and left of 0.

7. To graph a Quadratic Equation y = ax 2 +bx+cy = -ax 2 +bx+c If a is positive, the parabola opens up If a is negative, the parabola opens down

8. Graph Points Line of symmetry A is positive 1, so the parabola opens up with (0,0) as the low point.

9. GRAPH: y = x 2 -x-6 Identify the a, b, and c values First find the vertex Make a table with an x value to the right and left of the vertex x value Graph these points and connect. Label the vertex

10. Find vertex and plug in to find y. value to have high or low point. 1.

11. The x value of the vertex is 1 / 2 Now find the y value of the vertex by plugging x back into the equation. y = x 2 -x-6 y = ( 1 / 2 ) 2 – ½ - 6 The y value is - 25 / 4. Now pick a point to the left and right of ½.

12. GRAPH : y = x 2 -x-6 I try to pick points equal distance from the vertex x value. I also tried 0 here.

13. Vertex low Y=x 2 -x-6 opens up (a positive) line of symmetry x =

14. Line of Symmetry Graph: y= -2x 2 +2x+1 a is negative- opens down = 1 2 Find the y value, then pick a point to the left and right of 1/2 to see how to draw the parabola.

15. - 2 - - 2 2 2 -

16. y=-2x 2 +2x+1

17. Use parabola to find the height of a shot put. Height in feet Distance in feet 34.15 Vertex is height

18. Equation: y= -.01464x 2 +x+5 USE CALCULATOR!

19. Put x back in to find y value y = -.01464(34.15) 2 +34.15+5 = 22.08 ft. high (34.15,22.08) vertex (high point)