Graphing y = ax^2 + bx + c

1. Graphing y = ax 2 + bx + c By L.D.

2. Table of Contents

3. Formula

4. Summary

5. How to Find the the Direction the Graph Opens Towards

6. How to Find the y Intercept

7. How to Find the Vertex

8. How to Find the Axis of Symmetry

9. Problem 1

10. Problem 2

11. End

12. Formula y = ax 2 + bx + c

13. Summary In this presentation we are learning how to graph y = ax 2 + bx + c . We will graph this by first finding the direction it opens up, the y intercept, the vertex and the axis of symmetry. The next three slides are devoted to how to find these.

14. How to Find the the Direction the Graph Opens Towards y = a x 2 + bx + c Our graph is a parabola so it will look like or In our formula y = a x 2 + bx + c, if the a stands for a number over 0 (positive number ) then the parabola opens upward , if it stands for a number under 0 ( negative number ) then it opens downward .

15. How to Find the y Intercept y = ax 2 + bx + c The y intercept is a number that is not generally used as a vertex, it is used as one of the places to plot the line. It’s formula is (0, c ). The c is always a constant. The exception to it not being used as a vertex is when the b is equal to 0.

16. How to Find the Vertex y = a x 2 + b x + c The vertex has an x coordinate of – b /2 a To find the y coordinate one must place the x coordinate number into the places x occupies in the problem.

17. How to Find the Axis of Symmetry y = a x 2 + b x + c The line for the axis of symmetry crosses over the number achieved by doing the formula – b /2 a .

18. Problem 1 Formula: y = ax 2 + bx + c y = 5x 2 + 10x – 3 Directions: find the vertex, y-intercept and axis of symmetry. Then you may graph.

19. Problem 1 Formula: y = ax 2 + bx + c y = 5x 2 + 10x – 3 The first thing we will find is the vertex. As mentioned in slide 6, this is done by first finding the x coordinate using –b/ 2a. –b/ 2a = -10/2(5) = -10/10 = -1 Our x coordinate is -1. On the next slide we will find the y coordinate.

20. Problem 1 Formula: y = ax 2 + bx + c y = 5x 2 + 10x – 3 x coordinate: -1 As mentioned in slide 6, the y coordinate is found by placing the x coordinate in the places that x occupies in the problem. y = 5(-1) 2 + 10(-1) – 3 y = 5 + - 10 – 3 y = -8, so our y coordinate is -8, making our vertex located at (-1, -8).

21. Problem 1 Formula: y = ax 2 + bx + c y = 5x 2 + 10x – 3 Vertex: (-1, -8) Now we need to find the axis of symmetry, to do this we would use the same formula ( –b/2a ) as we used to get our x coordinate, so our axis of symmetry is -1.

22. Problem 1 Formula: y = ax 2 + bx + c y = 5x 2 + 10x – 3 Vertex: (-1, -8) Axis of symmetry: -1 The last step before graphing is where we need to find our y-intercept which will be the place that our vertex reaches too. We will do this by going to slide 6. The formula it gives us is (0, c), so our y-intercept is (0, -3).