1. Solving Quadratics Using a Graphing Calculator Created By: Ciondra Brown & Nathanial Harris

2. Graphing with the Calculator You Can Do That?!?! Of course you can, it is really simple and is easier than other methods. Here I’ll show you I already know how to graph it! Show me how to solve! Click here

3. Step By Step Process Note: Before you start, you should clear the memory of the calculator by pressing the 2 nd button then + then 7 then 1 then 2. Start by pressing the Y= button on the calculator Next, Enter your problem EXACTLY as shown BUT ONLY IF THE EQUATION IS EQAUL TO ZERO After that, hit the graph button. As easy as that.

4. Here’s an example 2x²-5x+3=0 Please graph the following equation using a graphing calculator Note: you can not enter “= 0” into the calculator. Enter the equation without it

5. If you did this correctly your graph should look like this;

6. Yea I already know how to do that but how do you solve it? I was just about to get to that. Here watch this.

7. Solving Quadratics Using a Graphing Calculator Now that you know the basics, lets get to the meat and potatoes

8. Something you should know It the graph touches the X-axis once than there is only one solution. If it touches twice than there are two solutions, and if it doesn’t touches the X- axis than there is no solution. Use this as a short cut

9. Now that you have graphed the equation and you are able to see it (Remember: if you cant see it, than the calculator can not find it) it is time to find the solution A.K.A. were the lines touch the X-axis. And here is how you do that. Press the 2 nd key then trace Now scroll down to were it says zero and hit enter

10. Time to pay attention Now you will have to hold your arrow key until it is on the left side of your equation and is above the X-axis then hit enter. Now move it to the left side of the equations making sure it is below the X-axis this time and hit enter twice.

11. Okay? Now what? After that, you will get were the line touches the X-axis (one solution) on the right side. You are now halfway done. Now all you need it the left side

12. Okay how do you get the left? Do almost the same thing to get the left one. Move the arrow to the right bellow the X-axis this time and press enter. Now move it to the right above the X-axis and press enter twice.

13. That’s it! Those two numbers are your solution. Now lets get some practice. Shall we?

14. Practice Problem Please find the solution for this problem using a graphing calculator 3x²-3x-3=0

15. Did I do this right? If you did it right your solution is and your graph should look like this. I didn’t get that. Where did I go wrong. Solution -3 and 0

16. Lets get in some practice Solve. Round if necessary 1)x²+3x-4=0 2)y²+y-42=0 3)k²+2k-24=0 4)b²+11b+24=0 5)r²-13r-48=0 6)5x²+3x-2=0 7)-6x²+3x-2=0 8)4x+5x²-10=0 9)2x²+1x=0 10)4x²-4x+4=0 Click for answers 1)Solution -4 and 1 2)Solution -7 and 6 3)Solution -6 and 4 4)Solution -3 and -8 5)Solution 16 and -3 6)Solution -1 and.4 7)No solution 8)Solution 1.87 and 1.07 9)Solution 0 10)No solution No cheating!!

17. Now that you got that… That was easy right? Ok hot shot, lets see how smart you are.

18. Lets say your equation is something like this 2x²-5x+13=44

19. Before you start to cry, let me show you how to do this

20. 2x²-5x+13=44 -44 -44 2x²-5x-31=0 Now you can graph it Original problem The equation needs to be equal to zero. Do the inverse, in this case subtract 44 Your new equation Enter the new equation into the graphing calculator

21. Lets do one more 1)x²=3x+15 2) x²=3x+15 -x² 3)0=-x²+3x+15 or -x²+3x+15=0 4)Graph your new equation 1.Original problem 2.This equation needs to be equal to zero. Do the inverse. 3.Your new equation 4.Put your new equation into the graphing calculator

22. Easy right? Ready for some more practice…? Great

23. Solve, round if necessary 1)n²-9n=-18 2)2z+z²=35 3)z²-24=16z 4)c²+6=-5c 5)t²+12t+2=0 6)3r²-9r=0 7)1/3x²+12x=-6 1)Soultion 3 and 6 2)Soltution 5 and -7 3)Solution -1.38 and 17.38 4)Solution -2 5)Soution -11.83 and -.17 6)Solution 3 and 0 7)No solution No cheating

24. Now that you know that you should know Sometimes you might see equations like this;(x-7)²=0 When you see this enter the equation the way it is shown but with parentages and without the “= 0” part

25. You now know how to graph quadratics using a graphing calculator The next slide has a printable graphing organize for you to have

27. Thanks and good luck For extras things having to do with this topic go to… http://webgraphing.com/graphing_basic.jsp http://quiz.econ.usyd.edu.au/mathquiz/quadratics/index.php http://www.quia.com/cb/24731.html http://www.algebra.com/tutors/solve_quadratic_equation.solv er http://www.purplemath.com/modules/grphquad.htm End of slide show

28. Check list Make sure you equation has the “²” symbol. Remember you can not enter “= 0” Make sure that you are following the steps on slides 10 and 111011