Solving Quadratics Solving Quadratics Using a Graphing Using a Graphing

CalculatorCalculator

Created By:Created By:

Ciondra BrownCiondra Brown

& Nathanial Harris& Nathanial Harris

Graphing with the Graphing with the CalculatorCalculator

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

Step By Step ProcessStep By Step ProcessNote: Before you start, you should clear the memory of the

calculator by pressing the 2nd button then + then 7 then 1 then 2.

Start by pressing the Y= button on the calculatorNext, Enter your problem EXACTLY as shown BUT ONLY IF

THE EQUATION IS EQAUL TO ZEROAfter that, hit the graph button. As easy as that.

Here’s an exampleHere’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

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

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.

SolvingSolving Quadratics Using a Quadratics Using a Graphing CalculatorGraphing Calculator

Now that you know the basics, lets get to the meat and potatoes

Something you should knowSomething 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

• 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 2nd key then trace Now scroll down to were it says zero and hit enter

Time to pay attention 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.

Okay? Now what?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

Okay how do you get the Okay how do you get the left?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.

That’s it!That’s it!

Those two numbers are your solution. Now lets get some practice. Shall we?

Practice ProblemPractice Problem

Please find the solution for this problem using a graphing calculator

3x²-3x-3=0

Did I do this right?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

Lets get in some practiceLets get in some practiceSolve. Round if necessary 1) x²+3x-4=02) y²+y-42=03) k²+2k-24=04) b²+11b+24=05) r²-13r-48=06) 5x²+3x-2=07) -6x²+3x-2=08) 4x+5x²-10=09) 2x²+1x=010)4x²-4x+4=0

Click for answers1) Solution -4 and 12) Solution -7 and 63) Solution -6 and 44) Solution -3 and -85) Solution 16 and -36) Solution -1 and .47) No solution8) Solution 1.87 and 1.079) Solution 010)No solution

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

No cheating!!

Now that you got that…Now that you got that…• That was easy right? Ok hot shot,

lets see how smart you are.

• Lets say your equation is something like this

• 2x²-5x+13=44

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

• 2x²-5x+13=44

• 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

Lets do one moreLets do one more1) x²=3x+15

2) x²=3x+15-x² -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

Easy right? Ready for some more practice…? Great

Solve, round if necessary Solve, round if necessary 1) n²-9n=-182) 2z+z²=353) z²-24=16z4) c²+6=-5c5) t²+12t+2=06) 3r²-9r=07) 1/3x²+12x=-6

1) Soultion 3 and 62) Soltution 5 and -73) Solution -1.38 and

17.38 4) Solution -25) Soution -11.83

and -.17 6) Solution 3 and 07) No solution

No cheating

No cheating

No cheatingNo cheating

No cheatingNo cheating

No cheating

Now that you know that you Now that you know that you should knowshould 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

• You now know how to graph quadratics using a graphing calculator

• The next slide has a printable graphing organize for you to have

Solving Quadratics w/ the Graphing Calculator

What Would the Parabola look like? a is Positive – opens Up ↑

a is a Large # - Narrow Parabola

a is Negative – opens Down ↓

a is a Small # - Wide Parabola

Beginning Entering your Problem REMEMBER: Clear the Memory before Starting your Problems. Step 1.) Press the Y= Button Step 2.) Enter your Problem Exactly as shown on Problem -Your Problem MUST be Equal to Zero before Entering

Solving

Once you have graphed your Problem: Step 1.) Press the 2nd Button Step 2.) Press the TRACE Button Step 3.) Then Go to :Zero and Press Enter Step 4.) Go to one place on the parabola where the x-axis or the closest place Step 5.) Then move the dot left ward of that spot and press enter Step 6.) Do Step 4 again but the go right ward instead and press enter Step 7.) Then your answer one of your answers should show up.

Thanks and good luckThanks and good luck• For extras things having to do with this topic go to…

http://webgraphing.com/graphing_basic.jsphttp://quiz.econ.usyd.edu.au/mathquiz/quadratics/index.php

http://www.quia.com/cb/24731.htmlhttp://www.algebra.com/tutors/solve_quadratic_equation.solver

http://www.purplemath.com/modules/grphquad.htm

End of slide show

Check list 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 11