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Intro to Quadratics

It’s hip to be squared

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Learning Goals

By the end of today I will be able to:

  • Make a table of values
  • Find the first and second differences of a function

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Back to Basics

Let’s review rules of addition and subtraction:

If the signs are the same:

  • Positive + Positive → Sum of values, Positive
  • Negative + Negative → Sum of values, Negative
  • Positive - Positive → Difference of values, + or -
  • Negative - Negative → Difference of values, + or -
  • Positive - Negative → Sum of values, Positive
  • Negative - Positive → Sum of values, Negative

Whatever… Let’s just go do some addition and subtraction…

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The Sum of All Fears

Find the sum of the following:

7 + 5

= 12

-3 + -12

= -15

8 - 17

= -9

6 - 5

= 1

-5 - -9

= 4

-13 - -6

= -7

9 + -5

= 4

6 + -8

= -2

-3 + 5

= 2

-9 + 1

= -8

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First Differences

Finding first differences means finding the difference between 2 consecutive y-values:

-10 - (-13) = -10 + 13 = 3

-7 - (-10) = -7 + 4 = 3

-4 - (-7) = -4 + 7 = 3

-1 - (-4) = -1 + 4 = 3

x

y

-2

-13

-1

-10

0

-7

1

-4

2

-1

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Quadratics and Differences

Finding second differences means finding the first differences then finding difference between 2 consecutive first differences.

​

x

y

-2

1

-1

-2

0

-3

1

-2

2

1

First Differences:

-2 - 1 = -3

-3 - (-2) = -1

-2 - (-3) = 1

1 - (-2) = 3

Second Differences:

-1 - (-3) = 2

1 - (-1) = 2

3 - 1 = 2

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Activity!

With your partner�1. Build the models shown on your experiment sheet plus�the next model in the sequence.�2. Complete the table of values (get it checked).�3. Find the First Differences and Second Differences for your�data.�4. Plot the points in your table of values on the graph provided.�5. Draw a "curve of best fit" through the points.�6. Find the other group that performed your experiment.�7. Recreate your table and graph on chart paper.

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Bring it all back

First Differences

  • If the first differences of a relationship are constant (the same number), that relationship is linear

Second Differences

  • If the second differences of a relationship are constant, that relationship is quadratic
  • If the second differences of a relationship are zero, that relationship is linear