Question

Select the correct answer. What is the standard form of this function?

[f(x) = -(x-4)^2 + 2]
a) (f(x) = x^2 + 8x - 14)
b) (f(x) = -x^2 + 8x - 14)
c) (f(x) = -x^2 + 4x - 30)
d) (f(x) = x^2 + 4x - 30)

Answer 1

The standard form of the function f(x) = -(x-4)^2 + 2 is f(x) = -x^2 + 8x - 14 (option b).

Step-by-step explanation:

The standard form of the function f(x) = -(x-4)^2 + 2 is f(x) = -x^2 + 8x - 14 (option b).

To convert the function to standard form, we need to expand and simplify the equation. Distributing the negative sign to each term inside the parentheses gives us f(x) = -x^2 + 8x - 16 + 2. Rearranging the terms in descending order of the exponent, we have f(x) = -x^2 + 8x - 14.