Successive Differences in Polynomials

When the 2nd differences are constant, the relationship is _________________.

• linear

• quadratic

• exponential

• linaer

Zach was making a table of 1st and 2nd differences for a quadratic function. Where is his mistake?

• What are you talking about? There's no mistake!

• He messed up on the first-first difference (red one). It should be a positive 2.

• He messed up on the second-first difference (blue one). It should be a positive 2.

• He messed up on the third-first difference (green one). It should also be -2.

Mary created the following table of first and second differences for a given list of x and y values. How can she use this list to determine what a, b, and c are for the quadratic equation (ax² + bx + c)? Mark all correct answers.

• c = -4 because that is the y value when x = 0.

• a = 1 because the second differences are always 2a on a quadratic equation and 2a = 2.

• b = 6 because a + b (the first-first difference) = 7, so 1 + b = 7

• This problem is unsolvable because you need a 3rd difference.

Consider that for a polynomial of nth degree, the nth differences in outputs will be constant. So for a ​ (a)   function, the ​ 1st difference is constant. For a ​ (b)   function, the 2nd difference is constant. For a ​ (c)   function the 3rd difference is constant and for a ​ (d)   function, the 4th difference is constant.

• linear

• quadratic

• cubic

• quartic

• 3x³ +8x

• x³+3x² +8x

• 2x² +8x

• x³-3x³ +8x²

Dan created the given table of first, second and third differences for a given set of x and y values.

• The polynomial must be cubic since the third differences are the same.

• The polynomial is 6th degree because the third differences are all 6.

• There are not enough data points yet to determine what degree the polynomial is.

• Dan made a mistake on his first differences. -6 -(-4) is -10.

When the 1st differences are equal, it is a ______ function.

• linear

• quadratic

• exponential

• cubic

What are the 1st differences?

• +8, so it is linear

• -8, so it is linear

• +2, so it is linear

• +8, so it is quadratic

When the 2nd differences are equal, it is a ______ function.

• linear

• quadratic

• exponential

• cubic

Which is NOT true?

• 1st differences are not equal

• 2nd differences are equal

• 1st differences are equal

• it is quadratic