Question

Consider the given quadratic equations: equation a: y = 3x�� - 6x + 21, equation b: y = 3x�� - 6x + 18, equation c: y = 3(x - 1)�� + 18, equation d: y = 3(x - 1)�� + 21. Complete the following statement: The equations are equivalent, and of those, which equation is in the form most useful for identifying the extreme value of the function it defines?

1) Equation a
2) Equation b
3) Equation c
4) Equation d

Answer 1

The equations are quadratic and differ in their constant terms. Equation c is in vertex form and is most useful for identifying the extreme value of the function it defines, with its vertex representing the minimum point.

Step-by-step explanation:

The given quadratic equations are:
Equation a: y = 3x² - 6x + 21
Equation b: y = 3x² - 6x + 18
Equation c: y = 3(x - 1)² + 18
Equation d: y = 3(x - 1)² + 21

All these equations are quadratic equations, but they differ in their constant terms. The equation in the form most useful for identifying the extreme value of the function it defines is equation c. This is because equation c is in vertex form, which allows us to easily identify the vertex as the extreme point of the function. The vertex of equation c is (1, 18), which represents the minimum point of the function.