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Graphing Parabolas without a graphing Calc!!

Graphing Parabolas without a graphing Calc!!. The road to success is always under construction!!. It is easier than you think!!. To graph parabolas what do you think the single most important point is that you should know? THE VERTEX It gives you a home base to work off of. What next?.

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Graphing Parabolas without a graphing Calc!!

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  1. Graphing Parabolas without a graphing Calc!! The road to success is always under construction!!

  2. It is easier than you think!! • To graph parabolas what do you think the single most important point is that you should know? • THE VERTEX • It gives you a home base to work off of.

  3. What next? • Once you identify your vertex, it is important that you plot at least four other points. • Where should these points be? • At least two should go on either side.

  4. But still where do they go? • To decide this, the easiest thing to do is use the step pattern. • What is the step pattern? • The step pattern is the pattern which tells you how much to go up or down for every one unit that you go over. • The step pattern is based off of the first differences in a quadratic.

  5. What are the first differences? • In the most basic quadratic y=x2the first differences are 1,3,5 • IMPORTANT • This means that for any parabola with an “a” of 1 or -1, it will follow the 1,3,5 step pattern. • You should memorize this!!

  6. An example would be handy Ex. Graph the following parabolas on the given grid y=x2 Y=-x2

  7. What if we change the a value • This is easy. • All we do is multiply the 1,3,5 step pattern by whatever the new “a” value is • For example if you have y=2x2, the step pattern would be 2,6,10 • For y = 0.5x2, the step pattern would be 0.5,1.5,2.5 • What would the step pattern be for y=3x2

  8. An example would be handy Graph the following on the grid provided Ex. y=2x2 Y=0.5x2 Y=-2x2

  9. Putting it all together • So what if we get an equation with all of the transformations? • Ex y=2(x-3)2-4 • Steps: • 1. Find the vertex • 2. Apply the step pattern

  10. Lets try it! Graph: y=2(x-3)2-4

  11. What if you get a values like 0.25 or 0.285? • Do you still use the step pattern? • Probably NOT. • In cases like this it is better to use a table of values.

  12. Example. • Graph f(x)=0.37(x+4)2-3 • Step 1. Plot the vertex • Step 2. Choose two values to plug in for x and then to solve for y.

  13. Example cont. f(x)=0.37(x+4)2-3 • I’ll choose to plug in -3 and -2 for x • F(-3)=-2.63. This means when I go one to the right of the vertex, the y value is -2.63 • By symmetry I also know that if I go one to the left of the vertex f(-5) =-2.63

  14. Example cont. f(x)=0.37(x+4)2-3 • Now go two to the right of the vertex. • F(-2)=-1.52. This means when I go two to the right of the vertex the y value is -1.52 • By symmetry if I go two to the left of the vertex, f(-6)=-1.52

  15. Lets graph it!

  16. Summary • For most parabolas you can simply use the step pattern and finish the graph very quickly • If the numbers involve long strings of decimals a table of values is probably more appropriate.

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