1. Quadratic equations Graphing and Solving with x 2

2. The typical form of a y = x 2 graph:

3. Quadratic equations Quick Exercise: Graph the following on the same axes: y = x 2 y = x 2 + 2 y = x 2 - 2x

4. The form of a y = x 2 + bx + c graph:

5. General Form of Quadratics The general form is either: y = ax 2 + bx + c Or ax 2 + bx + c = 0

6. General Form of Quadratics The general form is either: y = ax 2 + bx + cused for graphing Or ax 2 + bx + c = 0

7. General Form of Quadratics The general form is either: y = ax 2 + bx + cused for graphing Or ax 2 + bx + c = 0when solving for x For now, we will stick to when a = 1

8. Quadratics The equation for such a modified parabola is called a quadratic. Quadratics will always have a variable raised to the second power, like x 2. Factoring is one way to find solutions to quadratic equations. 0 = x 2 - 6x - 16 0 = (x - 8)(x + 2) x = {-2, 8}

9. D2. What are the solutions to the quadratic x 2 - 2x - 3 = 0? x 2 - 2x - 3 = 0 (x - 3)(x + 1) = 0 Set each factor to 0 x - 3 = 0 x = 3 x + 1 = 0 x = -1 x = -1 or x = 3  A. 1 and 3  B. -1 and -3  C. -1 and 3  D. 1 and -3  E. 1 and 2

10. So what about the y = x 2 - 2x - 3 graph?

12. The graph Crosses The x axis Here

13. So what about the y = x 2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1

14. So what about the y = x 2 - 2x - 3 graph? The graph Crosses The x axis And hereHere x = -1

15. So what about the y = x 2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1 And here x = 3

16. So what about the y = x 2 - 2x - 3 graph? The graph Crosses The x axis Here x = -1 And here x = 3 So again we see our solution, x = -1 or x = 3

17. So what about the y = ax 2 + bx + c graph? The graph Crosses The x axis Here x = ? And here x = ? This time we may need to use the quadratic formula