Question

select the correct answer.
which of the following statements is correct about quadratic number patterns?
a. the first difference is constant.
b. the third difference is greater than zero.
c. the second difference is constant.
d. the difference between terms is always positive.

Explanation:

To determine the correct statement about quadratic number patterns, we analyze each option:

• Option A: In a linear pattern, the first difference is constant. For a quadratic pattern, the first difference is not constant (it follows a linear pattern itself), so A is incorrect.
• Option B: Quadratic patterns have a constant second difference, and there is no third difference (or it is zero). So B is incorrect.
• Option C: By definition, for a quadratic sequence (which follows a quadratic function \( y = ax^2 + bx + c \)), the second difference (the difference of the first differences) is constant and equal to \( 2a \). So C is correct.
• Option D: The difference between terms in a quadratic pattern can be negative (e.g., for \( y = -x^2 + x \), the terms can decrease), so D is incorrect.

Answer:

C. The second difference is constant.