Section 1.5 Quadratic Equations

1. Section 1.5Quadratic Equations

3. Solving Quadratic Equations by Factoring

6. Example Solve by factoring:

7. Example Solve by factoring:

8. Example Solve by factoring:

9. Graphing Calculator The real solutions of a quadratic equation ax2+bx+c=0 correspond to the x-intercepts of the graph. The U shaped graph shown below has two x intercepts. When y=0, the value(s) of x will be the solution to the equation. Since y=0 these are called the zeros of the function.

10. Solving Polynomial Equations using the Graphing Calculator By pressing 2nd Trace to get Calc, then the #2,you get the zeros. It will ask you for left and right bounds, and then a guess. For left and right bounds move the blinking cursor (using the arrow keys-cursor keys) to the left and press enter. Then move the cursor to the right of the x intercept and press enter. Press enter when asked to guess. Then you get the zeros or solution. Repeat this process for each x intercept.

11. Solving Quadratic Equations by the Square Root Property

13. Example Solve by the square root property:

14. Example Solve by the square root property:

15. Completing the Square

17. Why we call this completing the square.

18. Example What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial.

19. Example Solve by Completing the Square:

20. Example Solve by Completing the Square:

21. Solving Quadratic Equations Using the Quadratic Formula

23. Example Solve by using the Quadratic Formula:

24. The Discriminant

26. Example Compute the discriminant and determine the number and type of solutions:

27. Determining Which Method to Use

29. Applications

32. Example

33. Example A 42 inch television is a television whose screen’s diagonal length is 42 inches. If a television’s screen height is 26 inches, find the width of the television screen 42 inches 26 inches

34. (a) (b) (c) (d)

35. (a) (b) (c) (d)