Question

Simplify the function f(x) = -2x^2 + 78 ,then determine which one is the key aspect of the function.

a The simplified base is: -2x² + 78
b The initial value is: 78
c The domain is: ℝ (all real numbers)
d all of the above

Answer 1

The function f(x) = -2x^2 + 78 is already in its simplest form, with the initial value being 78 and its domain being all real numbers (ℝ). The correct answer includes all aspects: the simplified base of the function, the initial value, and the domain.

Step-by-step explanation:

To simplify the function f(x) = -2x^2 + 78, we observe that it is already in its simplest form since there are no like terms to combine nor any factorizations or transformations that can be applied to simplify it further. When analyzing this function, we can identify several key aspects:

• The simplified base is indeed: -2x² + 78
• The initial value is the y-intercept, which is 78. This is the value of the function when x=0.
• The domain of any quadratic function is all real numbers, so the domain is ℝ (all real numbers).

Therefore, the correct answer includes all the listed options: simplified base, initial value, and domain.