Question

For a quadratic relation of the form ax² + bx + C, which of the following statements is true? *

A) The first differences are constant.
B) The second difference is constant.
C) The third difference is constant.
D) The ratio of the first and second differences is constant.

Answer 1

The second difference of a quadratic equation ax² + bx + c is constant, distinguishing it from other types of equations. To find the equation's solutions, we use the quadratic formula.

Step-by-step explanation:

For a quadratic equation of the form ax² + bx + c, the correct statement regarding its differences is that the second difference is constant. This means as you calculate the differences between consecutive y-values (obtained by substituting different x-values into the quadratic equation), the first differences will not be constant, but the second differences will be. This characteristic distinguishes a quadratic relationship from linear and other types of relationships.

In the given quadratic equation ax² + bx + c = 0, with constants a = 1.00, b = 10.0, and c = -200, to find its solutions (or roots), we apply the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).